3 added
3 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>195 Learners</p>
1
+
<p>225 Learners</p>
2
<p>Last updated on<strong>October 28, 2025</strong></p>
2
<p>Last updated on<strong>October 28, 2025</strong></p>
3
<p>Compound inequalities are two inequalities that are joined by the words "and" or "or". Each part is solved like a regular inequality, but the final answer depends on whether both conditions must be true (“and”) or just one needs to be true (“or”).</p>
3
<p>Compound inequalities are two inequalities that are joined by the words "and" or "or". Each part is solved like a regular inequality, but the final answer depends on whether both conditions must be true (“and”) or just one needs to be true (“or”).</p>
4
<h2>What is Compound Inequality?</h2>
4
<h2>What is Compound Inequality?</h2>
5
<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
5
<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
6
<p>▶</p>
6
<p>▶</p>
7
<p>A compound<a>inequality</a>merges two separate inequalities using the words “and” or “or”. Conjunction means both must hold simultaneously, like -1 < x < 3, while disjunction uses “or,” requiring at least one condition to be true.</p>
7
<p>A compound<a>inequality</a>merges two separate inequalities using the words “and” or “or”. Conjunction means both must hold simultaneously, like -1 < x < 3, while disjunction uses “or,” requiring at least one condition to be true.</p>
8
<p><strong>Study Strategy: </strong>Think of compound inequality as restrictions. Like if you are allowed to have<a>less than</a>three chocolate per day, then it can be said the<a>number</a>of chocolate you eat per day can be more than 0 but should be less than 3.</p>
8
<p><strong>Study Strategy: </strong>Think of compound inequality as restrictions. Like if you are allowed to have<a>less than</a>three chocolate per day, then it can be said the<a>number</a>of chocolate you eat per day can be more than 0 but should be less than 3.</p>
9
<p>This can be mathematically expressed as 0 < x < 3, where 'x' represents the number of chocolates you eat per day. </p>
9
<p>This can be mathematically expressed as 0 < x < 3, where 'x' represents the number of chocolates you eat per day. </p>
10
<h2>How to Represent Compound Inequalities in a Graph?</h2>
10
<h2>How to Represent Compound Inequalities in a Graph?</h2>
11
<p>To represent a compound inequality on a graph, follow the steps mentioned below:</p>
11
<p>To represent a compound inequality on a graph, follow the steps mentioned below:</p>
12
<ol><li><strong>Solve Each Inequality Separately</strong>For example, in the compound inequality x > 1 and x ≤ 4, treat each part as its own inequality and solve for x. </li>
12
<ol><li><strong>Solve Each Inequality Separately</strong>For example, in the compound inequality x > 1 and x ≤ 4, treat each part as its own inequality and solve for x. </li>
13
<li><strong>Plot Each Inequality on the Same Number Line</strong>After plotting, use open dots for strict inequalities (< or >) and closed dots for inclusive ones (≤ or ≥). Shade to the left for “<” or “≤” and to the right for “>” or “≥”. </li>
13
<li><strong>Plot Each Inequality on the Same Number Line</strong>After plotting, use open dots for strict inequalities (< or >) and closed dots for inclusive ones (≤ or ≥). Shade to the left for “<” or “≤” and to the right for “>” or “≥”. </li>
14
<li><strong>Combine the Shaded Regions</strong></li>
14
<li><strong>Combine the Shaded Regions</strong></li>
15
</ol><ul><li>AND (conjunction): Find the overlapping section (intersection) of both shaded regions. For example, x > 1 and x ≤ 4 gives the solution 1 < x ≤ 4.</li>
15
</ol><ul><li>AND (conjunction): Find the overlapping section (intersection) of both shaded regions. For example, x > 1 and x ≤ 4 gives the solution 1 < x ≤ 4.</li>
16
<li>OR (disjunction): Merge both regions (union). E.g., x < -1 or x > 2 gives the solution (-∞, -1] ∪ (2,∞). </li>
16
<li>OR (disjunction): Merge both regions (union). E.g., x < -1 or x > 2 gives the solution (-∞, -1] ∪ (2,∞). </li>
17
</ul><p>Let's practice this using a word problem</p>
17
</ul><p>Let's practice this using a word problem</p>
18
<p><strong>Practice Problem:</strong>Suppose you have $4, and you want to buy a toy. So, the<a>money</a>you can spend can be more than $0 or less than $4. Express these inequalities mathematically and on graph. </p>
18
<p><strong>Practice Problem:</strong>Suppose you have $4, and you want to buy a toy. So, the<a>money</a>you can spend can be more than $0 or less than $4. Express these inequalities mathematically and on graph. </p>
19
<p><strong>Solution:</strong> Lets represents the money with<a>variable</a>x.</p>
19
<p><strong>Solution:</strong> Lets represents the money with<a>variable</a>x.</p>
20
<ul><li>For x > 0, we will use open dot at 0.</li>
20
<ul><li>For x > 0, we will use open dot at 0.</li>
21
<li>For \( x \le 4\), we will use close dot at 4. </li>
21
<li>For \( x \le 4\), we will use close dot at 4. </li>
22
</ul><p>Expressing these<a>inequalities</a>on graph:</p>
22
</ul><p>Expressing these<a>inequalities</a>on graph:</p>
23
<p>The intersection of both regions will be the solution of \(0 < x \le 4\).</p>
23
<p>The intersection of both regions will be the solution of \(0 < x \le 4\).</p>
24
<h2>How to Solve Compound Inequalities?</h2>
24
<h2>How to Solve Compound Inequalities?</h2>
25
<p>For solving compound inequalities, students needs to follow the steps given below:</p>
25
<p>For solving compound inequalities, students needs to follow the steps given below:</p>
26
<ol><li>Recognize “AND” vs “OR”:<p>AND → solution is the overlap (intersection) OR → solution is the combined regions (union)</p>
26
<ol><li>Recognize “AND” vs “OR”:<p>AND → solution is the overlap (intersection) OR → solution is the combined regions (union)</p>
27
</li>
27
</li>
28
<li>Break the compound inequality into two separate inequalities(if needed). </li>
28
<li>Break the compound inequality into two separate inequalities(if needed). </li>
29
<li>Solve each part as usual. We need to isolate x while solving an inequality. However, when multiplying and dividing both sides by a negative<a>number</a>, we should flip the inequality sign. </li>
29
<li>Solve each part as usual. We need to isolate x while solving an inequality. However, when multiplying and dividing both sides by a negative<a>number</a>, we should flip the inequality sign. </li>
30
<li>Combine solutions: AND → take the intersection. OR → take a union. </li>
30
<li>Combine solutions: AND → take the intersection. OR → take a union. </li>
31
<li>(Optional) Graph on a<a>number line</a>to verify the solution.</li>
31
<li>(Optional) Graph on a<a>number line</a>to verify the solution.</li>
32
</ol><p>Let's practice these steps using problems</p>
32
</ol><p>Let's practice these steps using problems</p>
33
<p><strong>Practice Problem 1: </strong>Solve -2 < 2x + 4 < 3</p>
33
<p><strong>Practice Problem 1: </strong>Solve -2 < 2x + 4 < 3</p>
34
<p><strong>Explanation: Given Inequality: </strong>-2 < 2x + 4 < 3</p>
34
<p><strong>Explanation: Given Inequality: </strong>-2 < 2x + 4 < 3</p>
35
<ol><li>Subtract 4 on both sides \(-2 - 4 < 2x + 4 - 4 < 3 - 4\\ -6 < 2x < -1 \) </li>
35
<ol><li>Subtract 4 on both sides \(-2 - 4 < 2x + 4 - 4 < 3 - 4\\ -6 < 2x < -1 \) </li>
36
<li>Divide by 2 \(\frac{-6}{2} < \frac{2x}{2} < \frac{-1}{2} \\ -3 < x < \frac{-1}{2}\)</li>
36
<li>Divide by 2 \(\frac{-6}{2} < \frac{2x}{2} < \frac{-1}{2} \\ -3 < x < \frac{-1}{2}\)</li>
37
</ol><p>The solution is \(x = (-3, -\frac{1}{2})\) or \(x = (-\infty , - \frac{1}{2}) \cap (-3, \infty)\)</p>
37
</ol><p>The solution is \(x = (-3, -\frac{1}{2})\) or \(x = (-\infty , - \frac{1}{2}) \cap (-3, \infty)\)</p>
38
<p><strong>Practice Problem 2: </strong>Solve \(3 > 3x - 2 \ or\ -\frac{x}{2} + 4 < 3\)</p>
38
<p><strong>Practice Problem 2: </strong>Solve \(3 > 3x - 2 \ or\ -\frac{x}{2} + 4 < 3\)</p>
39
<p><strong>Explanation: Given Inequalities: </strong>\(3 > 3x - 2 \ or\ -\frac{x}{2} + 4 < 3\)</p>
39
<p><strong>Explanation: Given Inequalities: </strong>\(3 > 3x - 2 \ or\ -\frac{x}{2} + 4 < 3\)</p>
40
<ul><li><strong>Solving -3 > 3x - 2</strong> </li>
40
<ul><li><strong>Solving -3 > 3x - 2</strong> </li>
41
</ul><ol><li>Add 2 on both sides \(-3 + 2> 3x - 2 + 2\\ -1 > 3x\) </li>
41
</ul><ol><li>Add 2 on both sides \(-3 + 2> 3x - 2 + 2\\ -1 > 3x\) </li>
42
<li>Divide by 3 \(\frac{-1}{3} > \frac{3x}{3} \\ \frac{-1}{3} > x \)</li>
42
<li>Divide by 3 \(\frac{-1}{3} > \frac{3x}{3} \\ \frac{-1}{3} > x \)</li>
43
</ol><ul><li><strong>Solving \( - \frac{x}{2} + 4 < 3\)</strong> </li>
43
</ol><ul><li><strong>Solving \( - \frac{x}{2} + 4 < 3\)</strong> </li>
44
</ul><ol><li>Subtracting 4 in both sides: \(-\frac{x}{2} + 4 - 4 < 3 - 4 \\ -\frac{x}{2} < -1\) </li>
44
</ul><ol><li>Subtracting 4 in both sides: \(-\frac{x}{2} + 4 - 4 < 3 - 4 \\ -\frac{x}{2} < -1\) </li>
45
<li>Multiplying by -2 on both sides \(-2 \times -\frac{x}{2} < -1 \times -2 \\ x > 2\) </li>
45
<li>Multiplying by -2 on both sides \(-2 \times -\frac{x}{2} < -1 \times -2 \\ x > 2\) </li>
46
<li>Combining both inequality \( -\frac{1}{3} > x > 2\)</li>
46
<li>Combining both inequality \( -\frac{1}{3} > x > 2\)</li>
47
</ol><p>The solution is \(x = (- \infty, \frac{-1}{3})\cup (2, \infty)\)</p>
47
</ol><p>The solution is \(x = (- \infty, \frac{-1}{3})\cup (2, \infty)\)</p>
48
<h3>Explore Our Programs</h3>
48
<h3>Explore Our Programs</h3>
49
-
<p>No Courses Available</p>
50
<h2>Tips and Tricks to Master Compound Inequalities</h2>
49
<h2>Tips and Tricks to Master Compound Inequalities</h2>
51
<p>Students often find compound inequalities difficult and confusion at first. To ease the process, let’s focus on some tips and tricks to help you easily grasp the concept of compound inequalities.</p>
50
<p>Students often find compound inequalities difficult and confusion at first. To ease the process, let’s focus on some tips and tricks to help you easily grasp the concept of compound inequalities.</p>
52
<ol><li>Always make the changes on both sides of the inequality.</li>
51
<ol><li>Always make the changes on both sides of the inequality.</li>
53
<li>Remember,<a></a><a>addition</a>and<a></a><a>subtraction</a>on both sides of the inequality, doesn't change the sign.</li>
52
<li>Remember,<a></a><a>addition</a>and<a></a><a>subtraction</a>on both sides of the inequality, doesn't change the sign.</li>
54
<li>Always reverse the inequality sign when multiplying or dividing by a<a>negative number</a>.</li>
53
<li>Always reverse the inequality sign when multiplying or dividing by a<a>negative number</a>.</li>
55
<li>For x > a, shade the area outside 'a'.</li>
54
<li>For x > a, shade the area outside 'a'.</li>
56
<li>For x < a, shade the area inside 'a'. </li>
55
<li>For x < a, shade the area inside 'a'. </li>
57
</ol><p><strong>Parent Tip: </strong></p>
56
</ol><p><strong>Parent Tip: </strong></p>
58
<ul><li>Help children to correctly draw a shaded region on a graph.</li>
57
<ul><li>Help children to correctly draw a shaded region on a graph.</li>
59
<li>You can use real-life conditions for explaining inequalities efficiently.</li>
58
<li>You can use real-life conditions for explaining inequalities efficiently.</li>
60
<li>Encourage to solve problems from<a>compound inequality's</a><a>worksheet</a>.</li>
59
<li>Encourage to solve problems from<a>compound inequality's</a><a>worksheet</a>.</li>
61
</ul><h2>Common Mistakes and How to Avoid Them in Compound Inequalities</h2>
60
</ul><h2>Common Mistakes and How to Avoid Them in Compound Inequalities</h2>
62
<p>Students might make mistakes while dealing with compound inequalities. Some of these mistakes are common and can be avoided. Take a look at these common mistakes so that you can avoid them in the future. </p>
61
<p>Students might make mistakes while dealing with compound inequalities. Some of these mistakes are common and can be avoided. Take a look at these common mistakes so that you can avoid them in the future. </p>
63
<h2>Real-life Applications of Compound Inequalities</h2>
62
<h2>Real-life Applications of Compound Inequalities</h2>
64
<p>Compound inequalities are used in our daily life. It helps us in budgeting and monitoring speed limits and temperature ranges. We will be learning in the field of architecture, nature, biology, art, and design also. </p>
63
<p>Compound inequalities are used in our daily life. It helps us in budgeting and monitoring speed limits and temperature ranges. We will be learning in the field of architecture, nature, biology, art, and design also. </p>
65
<ol><li><strong>Biology:</strong>Biologists determine the temperature and pH ranges at which enzymes<a>function</a>optimally. For instance, an enzyme may function only when the pH is between 6 and 8. This can be modeled with an “and” compound inequality. </li>
64
<ol><li><strong>Biology:</strong>Biologists determine the temperature and pH ranges at which enzymes<a>function</a>optimally. For instance, an enzyme may function only when the pH is between 6 and 8. This can be modeled with an “and” compound inequality. </li>
66
<li><strong>Architecture</strong>: Structures such as the Tower of Light, inspired by mollusc shells, rely on compound inequalities: the material stress must not exceed its yield strength, and the deflection must stay within acceptable limits, ensuring safety and integrity. </li>
65
<li><strong>Architecture</strong>: Structures such as the Tower of Light, inspired by mollusc shells, rely on compound inequalities: the material stress must not exceed its yield strength, and the deflection must stay within acceptable limits, ensuring safety and integrity. </li>
67
<li><strong>Art & Design:</strong>The<a>golden ratio</a><a>sets</a>minimum and maximum bounds on<a>proportions</a>. The ratio between different parts of the Mona Lisa must lie between approximately 1.618 and its reciprocal, ensuring balanced composition. </li>
66
<li><strong>Art & Design:</strong>The<a>golden ratio</a><a>sets</a>minimum and maximum bounds on<a>proportions</a>. The ratio between different parts of the Mona Lisa must lie between approximately 1.618 and its reciprocal, ensuring balanced composition. </li>
68
<li><strong>Nature:</strong>Fractal Branching for Resource Transport, Tree and blood vessel systems follow fractal designs that balance branching depth (to reach all areas) without exceeding flow resistance, maintaining optimal transport efficiency. </li>
67
<li><strong>Nature:</strong>Fractal Branching for Resource Transport, Tree and blood vessel systems follow fractal designs that balance branching depth (to reach all areas) without exceeding flow resistance, maintaining optimal transport efficiency. </li>
69
<li><strong>Cross-disciplinary (Nature ↔ Built Environment):</strong>Hexagonal Honeycomb Efficiency in Architecture, Designs like the Eden Project use hexagonal structures that must fit within minimum material thickness while supporting maximum load, combining two inequality constraints for strength and lightness</li>
68
<li><strong>Cross-disciplinary (Nature ↔ Built Environment):</strong>Hexagonal Honeycomb Efficiency in Architecture, Designs like the Eden Project use hexagonal structures that must fit within minimum material thickness while supporting maximum load, combining two inequality constraints for strength and lightness</li>
70
-
</ol><h3>Problem 1</h3>
69
+
</ol><h2>Download Worksheets</h2>
70
+
<h3>Problem 1</h3>
71
<p>Solve -3 ≤ 2x -1 < 5</p>
71
<p>Solve -3 ≤ 2x -1 < 5</p>
72
<p>Okay, lets begin</p>
72
<p>Okay, lets begin</p>
73
<p>-1 ≤ x < 3 </p>
73
<p>-1 ≤ x < 3 </p>
74
<h3>Explanation</h3>
74
<h3>Explanation</h3>
75
<ol><li> Start with the compound inequality: -3 ≤ 2x -1 < 5 </li>
75
<ol><li> Start with the compound inequality: -3 ≤ 2x -1 < 5 </li>
76
<li>Add 1 to all three parts to isolate the term with x: -2 ≤ 2x < 6 </li>
76
<li>Add 1 to all three parts to isolate the term with x: -2 ≤ 2x < 6 </li>
77
<li>Divide all parts by 2: -1 ≤ x < 3</li>
77
<li>Divide all parts by 2: -1 ≤ x < 3</li>
78
</ol><p>Well explained 👍</p>
78
</ol><p>Well explained 👍</p>
79
<h3>Problem 2</h3>
79
<h3>Problem 2</h3>
80
<p>Solve 4x - 7 > 9 or 2x + 1 ≤ -3</p>
80
<p>Solve 4x - 7 > 9 or 2x + 1 ≤ -3</p>
81
<p>Okay, lets begin</p>
81
<p>Okay, lets begin</p>
82
<p>x > 4 or x ≤ -2 </p>
82
<p>x > 4 or x ≤ -2 </p>
83
<h3>Explanation</h3>
83
<h3>Explanation</h3>
84
<p>We’re given: 4x - 7 > 9 or 2x + 1 ≤ - 3</p>
84
<p>We’re given: 4x - 7 > 9 or 2x + 1 ≤ - 3</p>
85
<ul><li>Solve each part separately:</li>
85
<ul><li>Solve each part separately:</li>
86
</ul><ol><li>4x - 7 > 9 Add 7: 4x > 16 Divide by 4: x > 4 </li>
86
</ul><ol><li>4x - 7 > 9 Add 7: 4x > 16 Divide by 4: x > 4 </li>
87
<li>2x + 1 ≤ -3 Subtract 1: 2x ≤ -4 Divide by 2: x ≤ -2</li>
87
<li>2x + 1 ≤ -3 Subtract 1: 2x ≤ -4 Divide by 2: x ≤ -2</li>
88
</ol><ul><li>Combine using OR: Final Answer: x > 4 or x ≤ -2</li>
88
</ol><ul><li>Combine using OR: Final Answer: x > 4 or x ≤ -2</li>
89
</ul><p>Well explained 👍</p>
89
</ul><p>Well explained 👍</p>
90
<h3>Problem 3</h3>
90
<h3>Problem 3</h3>
91
<p>If 7 is less than 2x + 1 which is also at most 15, what can x be?</p>
91
<p>If 7 is less than 2x + 1 which is also at most 15, what can x be?</p>
92
<p>Okay, lets begin</p>
92
<p>Okay, lets begin</p>
93
<p> 3 < x ≤7 </p>
93
<p> 3 < x ≤7 </p>
94
<h3>Explanation</h3>
94
<h3>Explanation</h3>
95
<p>We’re given: 7 < 2x +1 ≤ 15</p>
95
<p>We’re given: 7 < 2x +1 ≤ 15</p>
96
<ul><li><strong>Step 1:</strong>Subtract 1 from all parts 6 < 2x ≤ 14 </li>
96
<ul><li><strong>Step 1:</strong>Subtract 1 from all parts 6 < 2x ≤ 14 </li>
97
<li><strong>Step 2:</strong>Divide all parts by 2 3 < x ≤ 7</li>
97
<li><strong>Step 2:</strong>Divide all parts by 2 3 < x ≤ 7</li>
98
</ul><p>Well explained 👍</p>
98
</ul><p>Well explained 👍</p>
99
<h3>Problem 4</h3>
99
<h3>Problem 4</h3>
100
<p>Solve -2 ≤ 4 -3x < 10</p>
100
<p>Solve -2 ≤ 4 -3x < 10</p>
101
<p>Okay, lets begin</p>
101
<p>Okay, lets begin</p>
102
<p>-2 < x ≤ 2 </p>
102
<p>-2 < x ≤ 2 </p>
103
<h3>Explanation</h3>
103
<h3>Explanation</h3>
104
<p> We’re solving the compound inequality: -2 ≤ 4 -3x < 10</p>
104
<p> We’re solving the compound inequality: -2 ≤ 4 -3x < 10</p>
105
<ul><li><strong>Step 1:</strong>Subtract 4 from all parts -6 ≤ -3x < 6</li>
105
<ul><li><strong>Step 1:</strong>Subtract 4 from all parts -6 ≤ -3x < 6</li>
106
</ul><ul><li><strong>Step 2:</strong>Divide all parts by -3, and flip the inequality signs 2 ≥ x > -2</li>
106
</ul><ul><li><strong>Step 2:</strong>Divide all parts by -3, and flip the inequality signs 2 ≥ x > -2</li>
107
</ul><ul><li>Rewriting in standard form: -2 < x ≤ 2</li>
107
</ul><ul><li>Rewriting in standard form: -2 < x ≤ 2</li>
108
</ul><p>Well explained 👍</p>
108
</ul><p>Well explained 👍</p>
109
<h3>Problem 5</h3>
109
<h3>Problem 5</h3>
110
<p>Solve 6x - 3 < 9 and 2x + 7 ≥ 3</p>
110
<p>Solve 6x - 3 < 9 and 2x + 7 ≥ 3</p>
111
<p>Okay, lets begin</p>
111
<p>Okay, lets begin</p>
112
<p> -2 ≤ x < 2 </p>
112
<p> -2 ≤ x < 2 </p>
113
<h3>Explanation</h3>
113
<h3>Explanation</h3>
114
<p>We’re solving a compound inequality using "and": 6x - 3 < 9 and 2x + 7 ≥ 3</p>
114
<p>We’re solving a compound inequality using "and": 6x - 3 < 9 and 2x + 7 ≥ 3</p>
115
<ul><li><strong>Solve each part:</strong></li>
115
<ul><li><strong>Solve each part:</strong></li>
116
</ul><ol><li>6x - 3 < 9 Add 3: 6x < 12 Divide by 6: x < 2 </li>
116
</ul><ol><li>6x - 3 < 9 Add 3: 6x < 12 Divide by 6: x < 2 </li>
117
<li>2x + 7 ≥ 3 Subtract 7: 2x ≥ -4</li>
117
<li>2x + 7 ≥ 3 Subtract 7: 2x ≥ -4</li>
118
<li>Divide by 2: x ≥ -2</li>
118
<li>Divide by 2: x ≥ -2</li>
119
</ol><ul><li>Combine using AND (overlap): Final answer: -2 ≤ x < 2</li>
119
</ol><ul><li>Combine using AND (overlap): Final answer: -2 ≤ x < 2</li>
120
</ul><p>Well explained 👍</p>
120
</ul><p>Well explained 👍</p>
121
<h2>FAQs Compound Inequalities</h2>
121
<h2>FAQs Compound Inequalities</h2>
122
<h3>1.How to explain compound inequalitiesto my child?</h3>
122
<h3>1.How to explain compound inequalitiesto my child?</h3>
123
<p>You can use objects or items to express compound inequalities for better visualization. Here is an example.</p>
123
<p>You can use objects or items to express compound inequalities for better visualization. Here is an example.</p>
124
<ul><li>Give your child 10 marbles, and ask to take out any number of marbles from 2 to 7. This is an example of AND.</li>
124
<ul><li>Give your child 10 marbles, and ask to take out any number of marbles from 2 to 7. This is an example of AND.</li>
125
<li>Now, in the second task, ask to take either marbles less than 3 or more than 6. This is an example of OR.</li>
125
<li>Now, in the second task, ask to take either marbles less than 3 or more than 6. This is an example of OR.</li>
126
</ul><h3>2.How can my child find if it's “and” or “or”?</h3>
126
</ul><h3>2.How can my child find if it's “and” or “or”?</h3>
127
<p>If the problem uses the words “and” or “or”, that’s clear to know what to do. But If written as -2 < x < 5, it implies ‘and’ (both conditions true simultaneously). </p>
127
<p>If the problem uses the words “and” or “or”, that’s clear to know what to do. But If written as -2 < x < 5, it implies ‘and’ (both conditions true simultaneously). </p>
128
<h3>3.How do I help my child graph inequalities?</h3>
128
<h3>3.How do I help my child graph inequalities?</h3>
129
<p>Explain these two points to your child.</p>
129
<p>Explain these two points to your child.</p>
130
<ul><li>For and, shade the overlapping region between endpoints.</li>
130
<ul><li>For and, shade the overlapping region between endpoints.</li>
131
<li>For or, shade all regions that satisfy either inequality (often two separate sections)</li>
131
<li>For or, shade all regions that satisfy either inequality (often two separate sections)</li>
132
</ul><h3>4.What happens if my child multiply or divide by a negative number?</h3>
132
</ul><h3>4.What happens if my child multiply or divide by a negative number?</h3>
133
<p>Children must flip the inequality sign when multiplying or dividing by a negative number. This happens due to the changes in order of number on a number line.</p>
133
<p>Children must flip the inequality sign when multiplying or dividing by a negative number. This happens due to the changes in order of number on a number line.</p>
134
<p>For example, -2x > 6 becomes x < -3 after dividing by -2. </p>
134
<p>For example, -2x > 6 becomes x < -3 after dividing by -2. </p>
135
<h3>5.How can I check my child's answer?</h3>
135
<h3>5.How can I check my child's answer?</h3>
136
<p>Test a value inside each proposed solution region to ensure it satisfies the original compound condition.</p>
136
<p>Test a value inside each proposed solution region to ensure it satisfies the original compound condition.</p>
137
<p>Graph it on a number line to visually verify correct shading. </p>
137
<p>Graph it on a number line to visually verify correct shading. </p>
138
138