Questions and Answers
What is the goal of solving linear equations in one variable?
To find the value of the variable that satisfies the given equation
In the equation X + 7 = 12, what is the first step to solve for X?
Transposing 7 to the other side of the equation, changing its sign to negative
What is the value of X in the equation 2X + 3 = 9?
X = 3
In the equation 3(X + 2) = 2, what is the first step to solve for X?
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What is the value of X in the equation (2X  3)/6 = X + 4?
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What is the purpose of crossmultiplication in the equation (2X  3)/6 = X + 4?
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What is represented by the two bars,  ?
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What is the absolute value of the number 5?
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What is the absolute value of the expression 8 + 10?
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What is the absolute value of the expression 15  3?
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What is the purpose of finding the absolute value of a number?
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What is the absolute value of the expression 14 + 6?
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Study Notes
Solving Linear Equations in One Variable
 The goal is to find the value of the variable that satisfies the given equation, also known as the solution.
Example 1: X + 7 = 12
 To solve, transpose 7 to the other side of the equation, changing its sign to negative.
 Simplify the equation: 12  7 = 5, so the value of x is 5.
Example 2: 2X + 3 = 9
 Transpose 3 to the other side, changing its sign to negative.
 Simplify the equation: 2X = 9  3, which equals 2X = 6.
 Divide both sides by 2 to solve for x: x = 6 ÷ 2 = 3.
Example 3: 3(X + 2) = 2
 Use the distributive property to multiply 3 with the terms inside the parenthesis.
 Simplify the equation: 3X + 6 = 2, which equals 3X = 2  6.
 Divide both sides by 3 to solve for x: x = 4 ÷ 3 = 4/3.
Example 4: (2X  3)/6 = X + 4

Method 1: Crossmultiplication
 Express the right side of the equation as a fraction: X + 4 = X/1 + 4/1.
 Crossmultiply: 6(X + 4) = 2X  3.
 Simplify the equation: 6X + 24 = 2X  3, which equals 4X = 27.
 Divide both sides by 4 to solve for x: x = 27 ÷ 4 = 27/4.

Method 2: Multiply the entire equation by 6 to eliminate the denominator.
 Simplify the equation: 2X  3 = 6X + 24.
 Combine like terms: 4X = 27.
 Divide both sides by 4 to solve for x: x = 27 ÷ 4 = 27/4.
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Description
Learn how to solve linear equations in one variable with examples of different types of equations. Practice solving for x with stepbystep explanations.