Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 31

{-4}

8y - 3 = 11y + 9 Step 1 : Collect variable terms on one side and constants on the other side. subtract 11 y from both the sides 8y - 3 - 11y= 11y + 9 - 11y Simplify -3 y -3 = 9 Add 3 on both the sides -3y -3 + 3 = 9 +3 Simplify -3y = 12 Divide both the sides by -3 $\frac{-3y}{-3}$ = $\frac{12}{-3}$ x =-4 Now we check the proposed solution, -4 , by replacing y with -4 in the original equation. Step 1: the original equation 8y - 3 = 11y + 9 Step2: Substitute -4 for y 8(-4)- 3 = 11 (-4) + 9 Step 3: Multiply 8.(-4) = -32, 11(-4) = -44 -32 - 3 = -44 + 9 Step 4: Solve -35 = -35 Since the check results in true statement, we conclude that the solution set of the given equation is {-4}