132 Chapter 2 Linear Equations and Inequalities Solving a Linear Equation Solve the equation. Solution: Subtract 3 from both sides.This isolates the x-term. Simplify. Simplify.The answer checks in the original equation. 2 2 3 1 1 5 1 5 1 5 x 3 x 3 3 x 5112 5 a1 5 1x 5 x 5 xb The solution is 5. 2 1 5 x 3 Example 2 Next, apply the multiplication property of equality to obtain a coefficient of 1 for x. Multiply both sides by 5. Skill Practice Solve the equation. 2. 2 1 2 a 7 Classroom Example: p. 138, Exercise 22 In Example 3, the variable x appears on both sides of the equation. In this case, apply the addition or subtraction property of equality to collect the variable terms on one side of the equation and the constant terms on the other side. Then use the multiplication or division property of equality to get a coefficient equal to 1. Solving a Linear Equation Solve the equation. Solution: 6x 4 2x 8 Subtract 2x from both sides leaving 0x on the right-hand side. Simplify. The x-terms have now been combined on one side of the equation. 6x 4 2x 8 6x 2x 4 2x 2x 8 4x 4 0x 8 4x 4 8 4x 4 4 8 4 4x 4 4x 4 x 1 The solution is 1. 4 4 Example 3 Add 4 to both sides of the equation. This combines the constant terms on the other side of the equation. To obtain a coefficient of 1 for x, divide both sides of the equation by 4. Simplify. The answer checks in the original equation. Skill Practice Solve the equation. 3. 10x 3 4x 2 Classroom Example: p. 138, Exercise 28 Answers 2. 18 3. 1 6
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