Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 32

{-1}

5y - 2 = 9y + 2 Step 1 : Collect variable terms on one side and constants on the other side. subtract 9y from both the sides 5y - 2 -9y = 9y + 2 -9y Simplify -4y -2 = 2 Add 2 on both the sides -4y -2 + 2 = 2 + 2 Simplify -4y = 4 Divide both the sides by -4 $\frac{-4y}{-4}$ = $\frac{4}{-4}$ y =-1 Now we check the proposed solution, -1 , by replacing y with -1 in the original equation. Step 1: the original equation 5y - 2 = 9y + 2 Step2: Substitute -1 for y 5(-1) - 2 = 9(-1) + 2 Step 3: Multiply 5(-1) = -5 , 9(-1) = -9 -5 - 2 = -9 +2 Step 4: Solve -7 = -7 Since the check results in true statement, we conclude that the solution set of the given equation is {-1}