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1 - <p>234 Learners</p>

1 + <p>270 Learners</p>

2 <p>Last updated on<strong>October 28, 2025</strong></p>

3 <p>A linear equation is a simple way to express a mathematical relationship. In a linear equation, ‘x’ represents the unknown quantity. This article explains linear equations in one variable in detail.</p>

4 <h2>What is Linear Equation in One Variable?</h2>

5 <p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

6 <p>▶</p>

7 <p>In a<a></a><a>linear equation</a>, each<a>variable</a>has a degree<a>of</a>exactly 1. A linear equation in one variable contains only a variable and results in just one solution.</p>

8 <ul><li>When we draw the linear equation, it makes a straight line. </li>

9 <li>Depending on the<a>equation</a>, the graph can be a slanted, horizontal, or vertical line.</li>

10 <li>The general form is ax + b = 0, where x is an unknown variable and a and b are<a>constants</a>. </li>

11 </ul><p><strong>For example</strong>, adding 7 to an unknown<a>number</a>gives 25. In this example, there is only one unknown variable. x + 7 = 25 </p>

12 <h2>Difference Between Linear Equation in One Variable vs Non-Linear Equations</h2>

13 <p><strong>Linear Equation</strong></p>

14 <p><strong>Non-Linear Equation</strong></p>

15 <p>It forms a straight line when plotted on a graph. </p>

16 <p>Non-linear equations create curves or other shapes on graphs.</p>

17 <p>A linear<a>equation</a>does not have<a>powers</a>or<a></a><a>exponents</a>.</p>

18 <p>These equations include higher powers like<a>squares</a>,<a></a><a>fractions</a>, and other powers like x2, y2, etc.</p>

19 <p>The highest<a>degree</a>of the linear equation is 1.</p>

20 <p>A non-linear equation has the highest degree of 2 or greater.</p>

21 <p>Linear equations are used for simple problems like finding speed, making budgets, or calculating total cost based on quantity.</p>

22 <p>Non-linear equations are used in physics,<a></a><a>geometry</a>, etc.</p>

23 <p><strong>Example</strong>: 3x + 2 = 8</p>

24 <p><strong>Example:</strong>x² + y² = 9</p>

25 <h2>How to Solve Linear Equations in One Variable?</h2>

26 <p>A linear equation in one variable has only one variable, and does not include squared<a>terms</a>or similar higher powers. The highest degree of such equations is 1.</p>

27 <p><a>Solving a linear equation</a>in one variable can be done using the following methods.</p>

28 <ol><li>Balancing Method</li>

29 <li>Transposition Method</li>

30 </ol><ul><li><strong>Balancing Method</strong></li>

31 </ul><p>In the balancing method, the equation is like a weighing scale; both sides must stay equal.</p>

32 <p>To<a>solve an equation</a> using balance method, we must do the same thing to both sides:</p>

33 <ol><li>Add the same number on both sides.</li>

34 <li>Subtract the same number from both sides</li>

35 <li>Multiply or divide both sides by the same non-zero number to solve for the variable.</li>

36 <li>Move the term to the other side by changing its sign.</li>

37 </ol><p><strong>Example:</strong>x - 3 = 7 Add 3 to both sides to eliminate the -3. $x - 3 + 3 = 7 + 3\\ x = 10$</p>

38 <ul><li><strong>Transposition Method</strong></li>

39 </ul><p>The transposition means moving a term from one side to the other side by changing its sign. </p>

40 <p><strong>Example:</strong>x + 5 = 12 Move 5 to the other side; it becomes -5. $x = 12 - 5\\ x = 7$ </p>

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43 <h2>Solving Equations With Variables on One Side</h2>

42 <h2>Solving Equations With Variables on One Side</h2>

44 <p>Some equations have variables on one side. To solve these, move the<a>number</a>to the other side, and use the opposite operations to isolate the variable.</p>

43 <p>Some equations have variables on one side. To solve these, move the<a>number</a>to the other side, and use the opposite operations to isolate the variable.</p>

45 <p>Let's understand this using few examples for practice.</p>

44 <p>Let's understand this using few examples for practice.</p>

46 <p><strong>Example 1</strong>: 2x - 4 = 10</p>

45 <p><strong>Example 1</strong>: 2x - 4 = 10</p>

47 <p><strong>Explanation:</strong></p>

46 <p><strong>Explanation:</strong></p>

48 <ol><li>Add 4 to both sides of the equation, $2x - 4 + 4= 10 + 4\\ 2x = 14$ </li>

47 <ol><li>Add 4 to both sides of the equation, $2x - 4 + 4= 10 + 4\\ 2x = 14$ </li>

49 <li>Perform<a></a><a>division</a>by 2 on both side. ${ 2x \over 2} = {14 \over 2} \\x = 7$</li>

48 <li>Perform<a></a><a>division</a>by 2 on both side. ${ 2x \over 2} = {14 \over 2} \\x = 7$</li>

50 </ol><p><strong>Example 2</strong>: ${2 \over 3} x + {3 \over 6} = 2$</p>

49 </ol><p><strong>Example 2</strong>: ${2 \over 3} x + {3 \over 6} = 2$</p>

51 <p><strong>Explanation:</strong></p>

50 <p><strong>Explanation:</strong></p>

52 <ol><li>Multiply both side by the LCM, which is 12 $12 \times {2 \over 3} x + 12 \times {3 \over 6} = 12 \times 2 \\ 8x + 6 = 24$ </li>

51 <ol><li>Multiply both side by the LCM, which is 12 $12 \times {2 \over 3} x + 12 \times {3 \over 6} = 12 \times 2 \\ 8x + 6 = 24$ </li>

53 <li>Perform<a>division</a>by 2 on both side. ${ 8x \over 2} + {6 \over 2} = {24 \over 2} \\ 4x + 3 = 12$ </li>

52 <li>Perform<a>division</a>by 2 on both side. ${ 8x \over 2} + {6 \over 2} = {24 \over 2} \\ 4x + 3 = 12$ </li>

54 <li>Move 3 to the other side $4x = 12 -3\\ 4x = 9$ </li>

53 <li>Move 3 to the other side $4x = 12 -3\\ 4x = 9$ </li>

55 <li>Divide both side by 4 ${4x \over 4} = {9 \over 4} \\ x = {9 \over 4}$</li>

54 <li>Divide both side by 4 ${4x \over 4} = {9 \over 4} \\ x = {9 \over 4}$</li>

56 </ol><h2>Tips and Tricks to Master Linear Equation in One Variable</h2>

55 </ol><h2>Tips and Tricks to Master Linear Equation in One Variable</h2>

57 <p>To understand and effenciently solve<a>linear equations in one variable</a>, here are a few tips and tricks:</p>

56 <p>To understand and effenciently solve<a>linear equations in one variable</a>, here are a few tips and tricks:</p>

58 <ol><li>Always perform<a></a><a>arithmetic</a> operations on both side of the equation. </li>

57 <ol><li>Always perform<a></a><a>arithmetic</a> operations on both side of the equation. </li>

59 <li>Simplify the equation first to make calculation easy. </li>

58 <li>Simplify the equation first to make calculation easy. </li>

60 <li>Don't forget the negative signs. </li>

59 <li>Don't forget the negative signs. </li>

61 <li>If the equations has fractions, eliminate them by multiplying the entire equation with the LCM. </li>

60 <li>If the equations has fractions, eliminate them by multiplying the entire equation with the LCM. </li>

62 <li>Remember the sign changes when the number moves to another side.<p>$+ \rightarrow - \\ - \rightarrow + \\ \times\rightarrow \div \\ \div\rightarrow \times $</p>

61 <li>Remember the sign changes when the number moves to another side.<p>$+ \rightarrow - \\ - \rightarrow + \\ \times\rightarrow \div \\ \div\rightarrow \times $</p>

63 </li>

62 </li>

64 </ol><p><strong>Parent Tip: </strong>Encourage your child to pratice problems from<a></a><a>worksheet</a>. Use real life examples to express linear equations to better visualize the linear equations</p>

63 </ol><p><strong>Parent Tip: </strong>Encourage your child to pratice problems from<a></a><a>worksheet</a>. Use real life examples to express linear equations to better visualize the linear equations</p>

65 <h2>Common Mistakes and How To Avoid Them in Linear Equations in One Variable</h2>

64 <h2>Common Mistakes and How To Avoid Them in Linear Equations in One Variable</h2>

66 <p>Students make mistakes when solving a linear equation in one variable. Here are some of the common mistakes and the ways to avoid them.</p>

65 <p>Students make mistakes when solving a linear equation in one variable. Here are some of the common mistakes and the ways to avoid them.</p>

67 <h2>Real Life Applications of Linear Equation in One Variable</h2>

66 <h2>Real Life Applications of Linear Equation in One Variable</h2>

68 <p>Linear equations in one variable are useful when only one unknown quantity needs to be found. Here are some real-life applications of linear equations.</p>

67 <p>Linear equations in one variable are useful when only one unknown quantity needs to be found. Here are some real-life applications of linear equations.</p>

69 <ol><li><strong>Finance and Budgeting:</strong>It is used to track expenses and income, calculate savings, or planning for future spending. If your income is fixed and expenses vary, a linear equation helps you to solve for what you can afford and how much you are left with.</li>

68 <ol><li><strong>Finance and Budgeting:</strong>It is used to track expenses and income, calculate savings, or planning for future spending. If your income is fixed and expenses vary, a linear equation helps you to solve for what you can afford and how much you are left with.</li>

70 <li><strong>Shopping and Retail:</strong>Retailers use linear equations to find<a></a><a>discounts</a>, final prices after applying discounts, offers, or adding<a>taxes</a>, and different charges.</li>

69 <li><strong>Shopping and Retail:</strong>Retailers use linear equations to find<a></a><a>discounts</a>, final prices after applying discounts, offers, or adding<a>taxes</a>, and different charges.</li>

71 <li><strong>Education and Exams:</strong>Linear equations help us determine the required scores, averages, or marks needed to improve grades.</li>

70 <li><strong>Education and Exams:</strong>Linear equations help us determine the required scores, averages, or marks needed to improve grades.</li>

72 <li><strong>Salaries:</strong>They are used to calculate the total pay, including bonus, overtime, and deductions while calculating salaries. </li>

71 <li><strong>Salaries:</strong>They are used to calculate the total pay, including bonus, overtime, and deductions while calculating salaries. </li>

73 - </ol><h3>Problem 1</h3>

72 + </ol><h2>Download Worksheets</h2>

73 + <h3>Problem 1</h3>

74 <p>Solve 2x + 5 = 13</p>

75 <p>Okay, lets begin</p>

76 <p>x = 4 </p>

77 <h3>Explanation</h3>

78 <ol><li>Subtract 5 from both sides<p>$2x + 5 = 13\\ 2x + 5 - 5 = 13 - 5\\ 2x = 8$</p>

79 </li>

80 <li>Divide both sides by 2<p>x = 4</p>

81 </li>

82 </ol><p>Well explained 👍</p>

83 <h3>Problem 2</h3>

84 <p>Solve 3x - 7 = 2x + 1</p>

85 <p>Okay, lets begin</p>

86 <p>x = 8 </p>

87 <h3>Explanation</h3>

88 <p>Move all the x terms to one side, and constants to another. </p>

89 <p>$3x - 7 = 2x + 1\\ \\ 3x - 2x = 1 + 7\\ x = 8$ </p>

90 <p>Well explained 👍</p>

91 <h3>Problem 3</h3>

92 <p>Solve x/3 + 2 = 5</p>

93 <p>Okay, lets begin</p>

94 <p>x = 9 </p>

95 <h3>Explanation</h3>

96 <ol><li>Subtract 2 from both sides<p>${x \over 3} + 2 = 5\\ {x \over 3} + 2 - 2 = 5 - 2\\ {x \over 3} = 3$</p>

97 </li>

98 <li>Multiply both sides by 3<p>$3 \times {x \over 3 } = 3 \times 3 \\x = 9$</p>

99 </li>

100 </ol><p>Well explained 👍</p>

101 <h3>Problem 4</h3>

102 <p>Solve 5(x - 2) = 3(x + 4)</p>

103 <p>Okay, lets begin</p>

104 <p>x = 11 </p>

105 <h3>Explanation</h3>

106 <ol><li>Expand both sides<p>$5(x - 2) = 3(x + 4)\\ 5x - 10 = 3x + 12$</p>

107 </li>

108 <li>Move x terms to one side<p>$5x - 3x = 12 + 10\\ 2x = 22$</p>

109 </li>

110 <li>Divide both sides by 2,<p>${2x \over 2} = {22 \over 2} \\ x = 11$</p>

111 </li>

112 </ol><p>Well explained 👍</p>

113 <h3>Problem 5</h3>

114 <p>Solve -4x + 9 = 5</p>

115 <p>Okay, lets begin</p>

116 <p>x = 1 </p>

117 <h3>Explanation</h3>

118 <ol><li>Subtract 9 from both sides<p>$-4x + 9 = 5 \\ -4x = -4$</p>

119 </li>

120 <li>Divide by -4<p>${ -4x \over -4} = {-4 \over -4} \\ x = 1$</p>

121 </li>

122 </ol><p>Well explained 👍</p>

123 <h2>FAQs on Linear Equation in One Variable</h2>

124 <h3>1.How to explain linear equation in one variable to a child?</h3>

125 <p>The linear equation in one variable is expressed as ax + b = 0, where x = variable and a,b are<a></a><a>real numbers</a>.</p>

126 <p>Use examples like, if two cookies cost $2, then cost of 1 cookies is given by 2x = $2, where x is the price of one cookie. </p>

127 <h3>2.Why is it important for my child to learn linear equations in one variable?</h3>

128 <p>It is important for your child beacause it builds the foundation of advance concepts of<a></a><a>algebra</a>, geometry in<a>maths</a>and can even be used to solve mathmatical problems based on daily life activities. </p>

129 <h3>3.What are some mistakes that my child can make in linear equations in one variable?</h3>

130 <p>Some mistakes your children can make are:</p>

131 <ol><li>Ignoring negative signs.</li>

132 <li>Not performing operations on both side.</li>

133 <li>Making calculation errors.</li>

134 <li>Not simplifying the equations. </li>

135 </ol><h3>4.How to explain difference between an equation and an expression to my child?</h3>

136 <p>An<a>expression</a>is a mathematical phrase like 2x + 3, but an equation includes an equal sign and shows a relationship like 2x + 5 = 15.</p>

137 <p>Explain this using examples, like finding the price of one candy, when the price of 10 candies is known, is an example of equation. Whereas finding the perimeter of a rectangular ground is given using expression 2(l + b). </p>

138 <h3>5.My child says linear equation can include powers other than 1. Is this correct?</h3>

139 <p>No, if the variable is squared, cubed, or raised to a higher power, it is not linear. Linear means the highest power is 1. </p>

140 <h2>Jaskaran Singh Saluja</h2>

141 <h3>About the Author</h3>

142 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

143 <h3>Fun Fact</h3>

144 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>