Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 40

{3}

7(3x - 2) + 5 = 6(2x - 1) + 24 Step 1 : Use distributive property 7.3x - 7.2 + 5 = 6.2x - 6 + 24 Multiply 21x - 14 + 5 = 12x -6+24 Solve 21x - 9 = 12x + 18 Step 2 : Collect variable terms on one side and constants on the other side. subtract 12x from both the sides 21x -9 -12x = 12x + 18 - 12x 9x - 9 = 18 Add 9 on both the sides 9x - 9 + 9 = 18 + 9 9x = 27 Divide both the sides by 9 $\frac{9x}{9}$ = $\frac{27}{9}$ x = 3 Now we check the proposed solution, 3 , by replacing x with 3 in the original equation. Step 1: the original equation 7(3x - 2) + 5 = 6(2x - 1) + 24 Step2: Substitute 3 for x 7(3.3 - 2) + 5 = 6(2.3 - 1) + 24 Step 3: Simplify 7(9 -2) +5 = 6(6-1) + 24 7(7) + 5 = 6(5) + 24 Multiply 7(7) = 49 , 6(5) = 30 49 + 5 = 30 + 24 Solve 54 = 54 Since the check results in true statement, we conclude that the solution set of the given equation is {3}