# Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2: 34

{1}

#### Work Step by Step

3(5 - x) = 4(2x + 1) Step 1 : Use distributive property 3.5 - 3x = 4.2x + 4 simplify 15 - 3x = 8x + 4 Step 2 : Collect variable terms on one side and constants on the other side. subtract 8x from both the sides 15 - 3x - 8x = 8x + 4 -8x Simplify 15 - 11x = 4 subtract 15 from both the sides 15 - 11x -15 = 4 -15 -11x = -11 Divide both the sides by -11 $\frac{-11x}{-11}$ = $\frac{-11}{-11}$ x = 1 Now we check the proposed solution, 1 , by replacing x with 1 in the original equation. Step 1: the original equation 3(5 - x) = 4(2x + 1) Step2: Substitute 1 for x 3(5 - 1) = 4(2.1 + 1) Step 3: Multiply 2.1 = 2 3(5-1) = 4(2+1) Step 4: Solve 3(4) = 4(3) Multiply 3(4) = 12, 4(3) = 12 12 = 12 Since the check results in true statement, we conclude that the solution set of the given equation is {1}

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