56 Chapter 2 Linear Equations and Inequalities in One Variable Objective 3 Examples Use the multiplication property of equality to solve each linear equation and check the answer. 3a. x 12 =-4 3b. 8 - 7a=-6 Solutions 3a. Since the variable x is divided by 12, we can multiply each side by 12 to isolate the variable. x 12 =-4 12¢ x 12 ≤ = 12(-4) Multiply each side by 12. x=-48 Simplify. Check: x 12 =-4 Begin with the original equation. -48 12 =-4 Replace x with -48. -4=-4 Simplify. The value -48 makes the equation true, so the solution set is 5-486. 3b. We first isolate the variable term on one side of the equation. 8 - 7a=-6 8 - 7a - 8=-6 - 8 Subtract 8 from each side. -7a=-14 Simplify. -7a 14 = --7 -7 Divide each side by -7. a = 2 Simplify. Check: 8 - 7a=-6 Begin with the original equation. 8 - 7(2)=-6 Replace a with 2. 8 - 14=-6 Simplify. -6=-6 Simplify. The value 2 makes the equation true, so the solution set is 526. Student Check 3 Use the multiplication property of equality to solve each linear equation and check the solution. a. y 5 =-2 b. -2 + 3y = 7 Solving Linear Equations Most equations we encounter cannot be solved by using only the addition property of equality or only the multiplication property of equality. Most will require us to apply both properties. The following strategy provides the steps for solving any linear equation. Objective 4 ▶ Solve linear equations.
hendricks_intermediate_algebra_1e_ch1_3
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