Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 37

{5}

3(x + 1) = 7(x - 2) - 3 Step 1 : Use distributive property 3.x + 3 = 7.x - 7.2 - 3 simplify 3x + 3 = 7x - 14 - 3 3x +3 = 7x -17 Step 2 : Collect variable terms on one side and constants on the other side. subtract 7x from both the sides 3x + 3 - 7x = 7x -17 -7x simplify -4x + 3 = -17 subtract 3 from both the sides -4x +3 - 3 = -17 -3 -4x = -20 Divide both the sides by -4 $\frac{-4x}{-4}$ = $\frac{-20}{-4}$ x = 5 Now we check the proposed solution, 5 , by replacing x with 5 in the original equation. Step 1: the original equation 3(x + 1) = 7(x - 2) - 3 Step2: Substitute 5 for x 3(5 + 1) = 7(5 - 2) - 3 Step 4: Solve 3(6) = 7(3) - 3 Multiply 3(6) = 3.6 = 18, 7(3)= 7.3 = 21 18 = 21 -3 18 = 18 Since the check results in true statement, we conclude that the solution set of the given equation is {5}