Artikel Matematika kelas 7 ini akan membahas persoalan sehari-hari menggunakan konsep Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV). Yuk, kita pelajari bersama!
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Ngomongin masalah Agustus-an, pasti kamu nggak asing lagi dengan bendera? Biasanya, sekolah akan mengadakan kegiatan lomba untuk menyemarakkan HUT Republik Indonesia. Ada lomba makan kerupuk, balap karung, tarik tambang, hingga memasukkan paku ke dalam botol.
Nah, kali ini, kakak mau mengajak kamu untuk memahami materi Matematika, lewat soal cerita yang ada kaitannya dengan lomba Agustus-an, nih. Simak cerita berikut, yuk!
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Saat acara lomba Agustus-an di sekolah, Rogu mendapat tugas untuk meletakkan bendera-bendera ke dalam suatu kotak. Tapi, satu kotak hanya bisa memuat kurang dari 65 buah bendera. Kalo dalam satu bungkus bendera, hanya berisi 10 buah bendera, kira-kira berapa sih jumlah maksimal bungkus bendera yang dapat masuk ke dalam kotak tersebut?
Permasalahan di atas, akan kita pecahkan menggunakan cara Sistem Pertidaksamaan Linear Satu Variabel. Wah, apa tuh?
Ilustrasi Hari Kemerdekaan (Sumber : Zonasultra.com)
Konsep Pertidaksamaan Linear Satu Variabel (PtLSV)
Pertidaksamaan Linier Satu Variabel (PtLSV) adalah pertidaksamaan yang hanya mempunyai satu variabel saja, misalnya variabel x. Pertidaksamaan ini, menggunakan salah satu tanda ketidaksamaan, yakni:
Tanda Ketidaksamaan
Dibaca atau Diartikan
>
Lebih besar dari
≥
Lebih besar sama dengan
<
Lebih kecil dari
≤
Lebih kecil sama dengan
Apa sih maksudnya? Oke kalau begitu, kita lihat contoh di bawah ini, ya:
Misalnya:
x < 5, berarti nilai x lebih kecil dari atau kurang dari 5, nggak termasuk angka 5 itu sendiri. Kalo dijabarkan, nilai x adalah 4, 3, 2, 1, 0, -1, …, dst.
atau,
x ≥ 7, berarti nilai x lebih besar sama dengan 7, termasuk angka 7 itu sendiri. Kalo dijabarkan, nilai x adalah 7, 8, 9, 10, 11, …, dst.
Gimana, sudah paham belum?
Baca Juga: Hubungan Antar Himpunan Matematika & Contohnya
Bentuk Umum Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV)
Seperti halnya Sistem Persamaan Linear Satu Variabel (SPLSV), pada Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV) juga terdapat bentuk umumnya, guys. Bentuk umum SPtLSV, yaitu:
ax + b < c
Keterangan:
a = koefisien x;
x = variabel; dan
b, c = konstanta.
Nah, kamu masih ingat nggak, apa bedanya variabel, koefisien, dan konstanta?
Variabel digunakan untuk menunjukkan nilai yang berubah. Kamu bisa menggunakan simbol berupa huruf, seperti a, b, x, y, z, dan sebagainya. Jadi, variabel tidak harus selalu x ya. Kemudian, konstanta merupakan nilai tetap (konsisten), dan koefisien merupakan faktor pengali dalam operasi Matematika.
Contoh:
3x + 1 > 2
Berarti, 3 merupakan koefisiennya, x merupakan variabelnya, 1 dan 2 merupakan konstantanya. Oh iya, tanda pertidaksamaan juga bisa menyesuaikan ya, misalnya “<”, “>”, “≤” atau “≥”.
Sifat-Sifat Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV)
Sebelum masuk ke cara menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel, kamu perlu tahu dulu nih mengenai sifat-sifat Sistem Pertidaksamaan Linear Satu Variabel, agar kamu tidak salah perhitungan. Berikut penjelasannya:
1. Tanda Pertidaksamaan Tidak Berubah pada Operasi Penjumlahan dan Pengurangan
Untuk menyelesaikan SPtLSV, terkadang kamu harus melakukan operasi penjumlahan atau pengurangan pada kedua ruas yang memiliki suku sama. Nah, operasi penjumlahan dan pengurangan, tidak akan mengubah tanda pertidaksamaan. Contoh:
x – 2 < 6 (kedua ruas sama-sama ditambah 2)
x – 2 + 2 < 6 + 2
x < 8
Sehingga, didapat nilai x < 8.
2. Tanda Pertidaksamaan Tidak Berubah pada Operasi Perkalian Positif
Sama halnya dengan operasi penjumlahan dan pengurangan, jika kedua ruas sama-sama dilakukan operasi perkalian positif, hal ini tidak akan mengubah tanda pertidaksamaan. Supaya kamu lebih paham, coba perhatikan contoh di bawah ini, deh:
2x + 4 > 6
Untuk menyelesaikan pertidaksamaan di atas, pertama-tama, kurangkan kedua ruas dengan -4.
2x + 4 – 4 > 6 – 4
2x > 2
Selanjutnya, kalikan kedua ruas dengan ½.
2x · ½ > 2 · ½
x > 1
Sehingga, didapat nilai x > 1.
3. Tanda Pertidaksamaan Berubah pada Operasi Perkalian Negatif
Nah, kalo kedua ruas dikalikan dengan bilangan negatif, maka ini akan menggantikan tanda pertidaksamaan, guys. Misalnya, dari yang awalnya <, berubah menjadi >, begitu juga sebaliknya. Kemudian, dari yang awalnya ≥, berubah menjadi ≤, begitu juga sebaliknya. Contoh:
-2x + 2 ≥ 0 (pertama-tama, kedua ruas sama-sama dikurangi 2)
-2x + 2 – 2 ≥ 0 – 2
-2x ≥ -2 (kemudian, kedua ruas sama-sama dikali -½)
-2x · -½ ≤ -2 · -½ (karena kedua ruas dikali bilangan negatif, maka tanda pertidaksamaannya berubah/dibalik)
x ≤ 1
Sehingga, didapat nilai x ≤ 1.
Baca Juga: Mengenal Operasi Hitung pada Pecahan
Cara Menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV)
Gimana nih? Sudah paham apa itu pengertian Pertidaksamaan Linear satu Variabel, bentuk dasar dari SPtLSV, dan juga sifat-sifatnya? Nah, kamu masih nggak dengan cerita Rogu di atas? Sekarang, kita bantu Rogu yuk untuk menyelesaikan masalah di kegiatan Agustus-an!
Bendera Agustus-an yang disiapkan Rogu untuk dimasukkan ke dalam kotak (Sumber: elruth.com)
Kita ulangi lagi yaaa ceritanya.
Rogu memiliki tugas untuk meletakkan beberapa bungkus bendera ke dalam suatu kotak. Tapi, satu kotak hanya bisa memuat kurang dari 65 buah bendera. Jika satu bungkus bendera, hanya berisi 10 buah bendera, berapa jumlah maksimal bungkus bendera yang dapat masuk ke dalam kotak tersebut?
Penyelesaian:
Pertama-tama, kita tentukan dulu variabelnya. Di sini, variabel yang belum diketahui adalah banyaknya bungkus bendera yang dapat dimasukkan ke dalam kotak, misalnya kita simbolkan dengan x.
Setelah itu, diketahui satu bungkus bendera berisi 10 buah bendera. Sementara satu kotak hanya dapat memuat kurang dari 65 buah bendera.
Nah, dari kedua pernyataan di atas, kita dapat tentukan model matematikanya, yaitu 10x < 65 yang dapat dibaca: “10 buah bendera dikali banyaknya bungkus yaitu kurang dari 65 buah bendera”.
Lain lagi nih, kalo semisal di dalam kotak sudah terisi 5 buah bendera. Maka, model matematikanya bisa kita tulis menjadi, 10x + 5 < 65 yang dapat dibaca: “10 buah bendera dikali banyaknya bungkus ditambah 5 bendera yaitu kurang dari 65 buah bendera”.
Terus, berapa sih jumlah maksimal bungkus bendera yang dapat masuk ke dalam kotak?
Oke, coba kita kerjakan sama-sama, ya!
10x + 5 < 65 (kedua ruas sama-sama dikurangi 5)
10x + 5 – 5 < 65 – 5
10x < 60 (kemudian, kedua ruas sama-sama dikali 1/10)
10x · 1/10 < 60 · 1/10
x < 6
Jadi, banyaknya bungkus bendera yang dapat masuk ke dalam kotak adalah 6 bungkus.
Baca Juga: Jenis-Jenis Bilangan Pecahan dan Contohnya
Supaya kamu lebih lancar lagi nih latihannya, simak beberapa langkah untuk menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV) di bawah ini, yuk!
Langkah-Langkah Menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV)
- Sederhanakan terlebih dahulu operasi yang ada. Berlaku juga pada operasi bertanda kurung.
- Gabungkan suku yang mengandung variabel yang sama ke dalam satu ruas.
- Selesaikan dahulu operasi penjumlahan atau pengurangan di kedua ruas dengan bilangan yang sama tanpa mengubah tanda ketidaksamaan.
- Kemudian, lanjut selesaikan operasi perkalian kedua ruas, dengan catatan: jika operasi perkalian dengan bilangan positif, maka tanda ketidaksamaan tidak berubah. Namun, jika operasi perkalian dengan bilangan negatif, maka tanda ketidaksamaan berubah.
So, apakah kamu mengerti dengan penjelasan materi Pertidaksamaan Linear Satu Variabel (PtLSV) yang sudah dibahas? Atau kamu masih belum puas dengan penjelasannya?
Hmm… tenang, kamu bisa nih belajar melalui video animasi di ruangbelajar. Di sana, kamu bisa belajar sekaligus latihan soal-soal. Selain itu, waktu belajar kamu akan lebih efektif, dan tidak akan menyita waktu bermain kamu. Jadiii tunggu apa lagi? Buruan download aplikasi ruangguru!
Referensi:
As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VII Semester I. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud
Sumber Foto:
Ilustrasi ‘Hari Kemerdekaan’ [Daring]. Tautan: https://zonasultra.com/gelar-festival-musik-kemerdekaan-cara-pemuda-pemudi-konawe-peringati-hut-ri-ke-71.html/ilustrasi-hari-kemerdekaan (Diakses: 21 Desember 2020)
Ilustrasi ‘Bendera Kemerdekaan’ [Daring]. Tautan: https://www.elruth.com/2017/08/aksesoris-unik-dan-menarik-yang.html (Diakses: 21 Desember 2020)
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<h1 class="content-title">
Cara Menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV) | Matematika Kelas 7 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/thalitha-ariesti-widhia" class="">Thalitha Ariesti Widhia</a> </p>
<p class="content-info"><span>November 19, 2024 • </span> <span>6 minutes read</span></p>
<br />
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<p><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/b9151f1e-bad3-4266-91f9-12ac25bbc856.png" alt="cara menyelesaikan sistem pertidaksamaan linear satu variabel" /></p>
<blockquote>
<p style="text-align: center;"><em style="text-align: center;"><strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-7">Artikel Matematika kelas 7</a></strong> ini akan membahas persoalan sehari-hari menggunakan konsep <strong>Sistem</strong> <strong>Pertidaksamaan Linear Satu Variabel (SPtLSV)</strong>. Yuk, kita pelajari bersama!</em></p>
</blockquote>
<p style="text-align: center;">—</p>
<p> </p>
<p style="text-align: justify;"><em>Ngomongin</em> masalah Agustus-an, pasti kamu nggak asing lagi dengan bendera? Biasanya, sekolah akan mengadakan kegiatan lomba untuk menyemarakkan HUT Republik Indonesia. Ada lomba makan kerupuk, balap karung, tarik tambang, hingga memasukkan paku ke dalam botol.</p>
<p style="text-align: justify;">Nah, kali ini, kakak mau mengajak kamu untuk memahami materi Matematika, lewat soal cerita yang ada kaitannya dengan lomba Agustus-an, nih. Simak cerita berikut, yuk!</p>
<p>—</p>
<p style="text-align: justify;">Saat acara lomba Agustus-an di sekolah, Rogu mendapat tugas untuk meletakkan bendera-bendera ke dalam suatu kotak. Tapi, satu kotak hanya bisa memuat kurang dari 65 buah bendera. Kalo dalam satu bungkus bendera, hanya berisi 10 buah bendera, kira-kira berapa sih jumlah maksimal bungkus bendera yang dapat masuk ke dalam kotak tersebut?</p>
<p style="text-align: justify;">Permasalahan di atas, akan kita pecahkan menggunakan cara <strong>Sistem Pertidaksamaan Linear Satu Variabel</strong>. Wah, apa tuh?</p>
<p style="text-align: center;"><img decoding="async" style="width: 600px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/agustusan%20fix%20no%20blur.jpg" alt="istem Pertidaksamaan Linear Satu Variabel" width="600" /></p>
<p style="text-align: center;"><em>Ilustrasi Hari Kemerdekaan (Sumber : Zonasultra.com)</em></p>
<p> </p>
<h2><span style="font-size: 18pt;">Konsep Pertidaksamaan Linear Satu Variabel (PtLSV)</span></h2>
<p style="text-align: justify;">Pertidaksamaan Linier Satu Variabel (PtLSV) adalah <strong>pertidaksamaan yang hanya mempunyai satu variabel saja, misalnya variabel x. </strong>Pertidaksamaan ini, menggunakan salah satu<strong> tanda ketidaksamaan</strong>, yakni:</p>
<table style="border-collapse: collapse; width: 100%;">
<tbody>
<tr>
<td style="width: 50%; text-align: center;"><strong>Tanda Ketidaksamaan</strong></td>
<td style="width: 50%; text-align: center;"><strong>Dibaca atau Diartikan</strong></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: 14pt;">></span></td>
<td style="width: 50%; text-align: center;">Lebih besar dari</td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: 14pt;">≥</span></td>
<td style="width: 50%; text-align: center;">Lebih besar sama dengan</td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: 14pt;"><</span></td>
<td style="width: 50%; text-align: center;">Lebih kecil dari</td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: 14pt;">≤</span></td>
<td style="width: 50%; text-align: center;">Lebih kecil sama dengan</td>
</tr>
</tbody>
</table>
<p> </p>
<p style="text-align: justify;">Apa sih maksudnya? Oke kalau begitu, kita lihat contoh di bawah ini, ya:</p>
<p>Misalnya:</p>
<p style="text-align: justify;">x < 5, berarti nilai x <em>lebih kecil dari</em> atau <em>kurang dari</em> 5, nggak termasuk angka 5 itu sendiri. Kalo dijabarkan, nilai x adalah 4, 3, 2, 1, 0, -1, …, dst.</p>
<p>atau,</p>
<p style="text-align: justify;">x <span style="font-size: 12pt;">≥ 7, berarti nilai x <em>lebih besar sama dengan</em> 7, termasuk angka 7 itu sendiri. Kalo dijabarkan, nilai x adalah 7, 8, 9, 10, 11, …, dst.</span></p>
<p>Gimana, sudah paham belum?</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-7-hubungan-antarhimpunan-matematika">Hubungan Antar Himpunan Matematika & Contohnya</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">Bentuk Umum Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV)</span></h2>
<p style="text-align: justify;"><span style="background-color: transparent;">Seperti halnya Sistem Persamaan Linear Satu Variabel (SPLSV)</span><strong style="background-color: transparent;"><em>, </em></strong>pada <span style="background-color: transparent;">Sistem Pertidaksamaan Linear Satu Variabel (</span><span style="background-color: transparent;">SPtLSV) juga terdapat bentuk umumnya, <em>guys</em>. Bentuk umum SPtLSV, yaitu:</span></p>
<p style="text-align: center;"><strong><span style="font-size: 14pt;">ax + b < c</span></strong></p>
<p>Keterangan:</p>
<p>a = koefisien x;</p>
<p>x = variabel; dan</p>
<p>b, c = konstanta.</p>
<p> </p>
<p>Nah, kamu masih ingat nggak, apa bedanya variabel, koefisien, dan konstanta?</p>
<p style="text-align: justify;">Variabel digunakan untuk menunjukkan nilai yang berubah. Kamu bisa menggunakan simbol berupa huruf, seperti a, b, x, y, z, dan sebagainya. Jadi, variabel tidak harus selalu x ya. Kemudian, konstanta merupakan nilai tetap (konsisten), dan koefisien merupakan faktor pengali dalam operasi Matematika.</p>
<p><strong>Contoh:</strong></p>
<p>3x + 1 > 2</p>
<p style="text-align: justify;">Berarti, 3 merupakan koefisiennya, x merupakan variabelnya, 1 dan 2 merupakan konstantanya. Oh iya, tanda pertidaksamaan juga bisa menyesuaikan ya, misalnya “<”, “>”, “≤” atau “≥”.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Sifat-Sifat Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV)</span></h2>
<p style="text-align: justify;">Sebelum masuk ke cara menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel, kamu perlu tahu dulu nih mengenai sifat-sifat Sistem Pertidaksamaan Linear Satu Variabel, agar kamu tidak salah perhitungan. Berikut penjelasannya:</p>
<p> </p>
<h3><span style="font-size: 14pt;">1. Tanda Pertidaksamaan Tidak Berubah pada Operasi Penjumlahan dan Pengurangan</span></h3>
<p style="text-align: justify;">Untuk menyelesaikan SPtLSV, terkadang kamu harus melakukan operasi penjumlahan atau pengurangan pada kedua ruas yang memiliki suku sama. Nah, operasi penjumlahan dan pengurangan, tidak akan mengubah tanda pertidaksamaan. Contoh:</p>
<p>x – 2 < 6 (kedua ruas sama-sama ditambah 2)<br />
x – 2 + 2 < 6 + 2<br />
x < 8</p>
<p>Sehingga, didapat nilai x < 8.</p>
<p> </p>
<h3><span style="font-size: 14pt;">2. Tanda Pertidaksamaan Tidak Berubah pada Operasi Perkalian Positif</span></h3>
<p style="text-align: justify;">Sama halnya dengan operasi penjumlahan dan pengurangan, jika kedua ruas sama-sama dilakukan operasi perkalian positif, hal ini tidak akan mengubah tanda pertidaksamaan. Supaya kamu lebih paham, coba perhatikan contoh di bawah ini, deh:</p>
<p>2x + 4 > 6</p>
<p style="text-align: justify;">Untuk menyelesaikan pertidaksamaan di atas, pertama-tama, kurangkan kedua ruas dengan -4.</p>
<p>2x + 4 – 4 > 6 – 4</p>
<p>2x > 2</p>
<p>Selanjutnya, kalikan kedua ruas dengan ½.</p>
<p>2x · ½ > 2 · ½</p>
<p>x > 1</p>
<p>Sehingga, didapat nilai x > 1.</p>
<p> </p>
<h3><span style="font-size: 14pt;">3. Tanda Pertidaksamaan Berubah pada Operasi Perkalian Negatif</span></h3>
<p style="text-align: justify;">Nah, kalo kedua ruas dikalikan dengan bilangan negatif, maka ini akan menggantikan tanda pertidaksamaan, <em>guys</em>. Misalnya, dari yang awalnya <, berubah menjadi >, begitu juga sebaliknya. Kemudian, dari yang awalnya ≥, berubah menjadi ≤, begitu juga sebaliknya. Contoh:</p>
<p>-2x + 2 ≥ 0 (pertama-tama, kedua ruas sama-sama dikurangi 2)</p>
<p>-2x + 2 – 2 ≥ 0 – 2</p>
<p>-2x ≥ -2 (kemudian, kedua ruas sama-sama dikali -½)</p>
<p>-2x · -½ <strong>≤</strong> -2 · -½ (karena kedua ruas dikali bilangan negatif, maka tanda pertidaksamaannya berubah/dibalik)</p>
<p>x <strong>≤</strong> 1</p>
<p>Sehingga, didapat nilai x <strong>≤</strong> 1.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-7-mengenal-operasi-hitung-pada-pecahan">Mengenal Operasi Hitung pada Pecahan</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">Cara Menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel </span><span style="font-size: 18pt;">(SPtLSV)</span></h2>
<p style="text-align: justify;">Gimana nih? Sudah paham apa itu pengertian Pertidaksamaan Linear satu Variabel, bentuk dasar dari SPtLSV, dan juga sifat-sifatnya? Nah, kamu masih nggak dengan cerita Rogu di atas? Sekarang, kita bantu Rogu yuk untuk menyelesaikan masalah di kegiatan Agustus-an!</p>
<p style="text-align: center;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bendera%20kotak.png" alt="Sistem Pertidaksamaan Linear Satu Variabel" width="600" /></p>
<p style="text-align: center;"><em>Bendera Agustus-an yang disiapkan Rogu untuk dimasukkan ke dalam kotak (Sumber: elruth.com)</em></p>
<p> </p>
<p>Kita ulangi lagi yaaa ceritanya.</p>
<p style="text-align: justify;"><span style="background-color: transparent;">Rogu memiliki tugas untuk meletakkan beberapa bungkus bendera ke dalam suatu kotak. Tapi, satu kotak hanya bisa memuat kurang dari 65 buah bendera. Jika satu bungkus bendera, hanya berisi 10 buah bendera, berapa jumlah maksimal bungkus bendera yang dapat masuk ke dalam kotak tersebut?</span></p>
<p><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;">Pertama-tama,<strong style="background-color: transparent;"> kita tentukan dulu variabelnya</strong><span style="background-color: transparent;">. Di sini, </span><strong style="background-color: transparent;">variabel yang belum diketahui </strong><span style="background-color: transparent;">adalah </span><strong style="background-color: transparent;">banyaknya bungkus bendera yang dapat dimasukkan ke dalam kotak</strong>, misalnya<span style="background-color: transparent;"> kita simbolkan dengan x. </span></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Setelah itu, diketahui satu bungkus bendera berisi 10 buah bendera. Sementara satu kotak hanya dapat memuat kurang dari 65 buah bendera. </span></p>
<p style="text-align: justify;">Nah, dari kedua pernyataan di atas<strong style="background-color: transparent;">, kita dapat tentukan model matematikanya</strong><span style="background-color: transparent;">, yaitu 10x < 65 yang dapat dibaca: “10 buah bendera dikali banyaknya bungkus yaitu kurang dari 65 buah bendera”.</span></p>
<p style="text-align: justify;">Lain lagi nih, kalo semisal di dalam kotak sudah terisi 5 buah bendera. Maka, model matematikanya bisa kita tulis menjadi, 10x + 5 < 65 yang dapat dibaca: “10 buah bendera dikali banyaknya bungkus ditambah 5 bendera yaitu kurang dari 65 buah bendera”.</p>
<p>Terus, berapa sih jumlah maksimal bungkus bendera yang dapat masuk ke dalam kotak?</p>
<p>Oke, coba kita kerjakan sama-sama, ya!</p>
<p>10x + 5 < 65 (kedua ruas sama-sama dikurangi 5)</p>
<p>10x + 5 – 5 < 65 – 5</p>
<p>10x < 60 (kemudian, kedua ruas sama-sama dikali 1/10)</p>
<p>10x · 1/10 < 60 · 1/10</p>
<p>x < 6</p>
<p>Jadi, banyaknya bungkus bendera yang dapat masuk ke dalam kotak adalah 6 bungkus.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/jenis-jenis-bilangan-pecahan">Jenis-Jenis Bilangan Pecahan dan Contohnya</a></strong></p>
<p> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Supaya kamu lebih lancar lagi nih latihannya, simak beberapa langkah untuk menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel (SPtLSV) di bawah ini, yuk!</span></p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;"><strong>Langkah-Langkah Menyelesaikan Sistem Pertidaksamaan Linear Satu Variabel </strong>(SPtLSV)</span></h2>
<ol style="text-align: justify;">
<li>Sederhanakan terlebih dahulu operasi yang ada. Berlaku juga pada operasi bertanda kurung.</li>
<li>Gabungkan suku yang mengandung variabel yang sama ke dalam satu ruas.</li>
<li>Selesaikan dahulu operasi penjumlahan atau pengurangan di kedua ruas dengan bilangan yang sama tanpa mengubah tanda ketidaksamaan.</li>
<li>Kemudian, lanjut selesaikan operasi perkalian kedua ruas, dengan catatan: jika operasi perkalian dengan bilangan positif, maka tanda ketidaksamaan tidak berubah. Namun, jika operasi perkalian dengan bilangan negatif, maka tanda ketidaksamaan berubah.</li>
</ol>
<p> </p>
<p style="text-align: justify;"><em>So</em>, apakah kamu mengerti dengan penjelasan materi <strong>Pertidaksamaan Linear Satu Variabel (PtLSV) </strong>yang sudah dibahas? Atau kamu masih belum puas dengan penjelasannya?</p>
<p style="text-align: justify;"><em>Hmm…</em> tenang, kamu bisa <em>nih</em> belajar melalui video animasi di <a href="/ruangbelajar" rel="noopener"><span style="font-weight: bold;">ruangbelajar</span></a>. Di sana, kamu bisa belajar sekaligus latihan soal-soal. Selain itu, waktu belajar kamu akan lebih efektif, dan tidak akan menyita waktu bermain kamu. Jadiii tunggu apa lagi? Buruan <em>download</em> <strong>aplikasi ruangguru!</strong></p>
<p><a href="https://app.ruangguru.com/ruangbelajar/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/a2dbab8e-e903-4b70-ae04-39ff5807647e.jpg" alt="CTA ruangbelajar" /></a></p>
<p><strong>Referensi:</strong></p>
<p style="text-align: left;">As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VII Semester I. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud</p>
<p style="text-align: left;"><strong>Sumber Foto:</strong></p>
<p style="text-align: left;">Ilustrasi ‘Hari Kemerdekaan’ [Daring]. Tautan: https://zonasultra.com/gelar-festival-musik-kemerdekaan-cara-pemuda-pemudi-konawe-peringati-hut-ri-ke-71.html/ilustrasi-hari-kemerdekaan (Diakses: 21 Desember 2020)</p>
<p style="text-align: left;">Ilustrasi ‘Bendera Kemerdekaan’ [Daring]. Tautan: https://www.elruth.com/2017/08/aksesoris-unik-dan-menarik-yang.html (Diakses: 21 Desember 2020)</p>
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<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>