Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2: 24

Answer

{7}

Work Step by Step

11x - (6x - 5) = 40 Step 1 : Drop parentheses and change the sign of each term in parentheses: - (6x - 5) = -6x + 5 11x - 6x +5 =40 Step 2: Combine like terms 11x - 6x = (11-6)x =5x 5x + 5 = 40 Step 3: subtract 5 from both the sides 5x+ 5 - 5 =40 -5 Step 4: Simplify 5x = 35 Step 5: Divide both the sides by 5 $\frac{5x}{5}$ = $\frac{35}{5}$ Step 6: Simplify x = 7 Now we check the proposed solution,7 , by replacing x with 7 in the original equation. Step 1: the original equation 11x - (6x -5) = 40 Step2: Substitute 7 for x 11.7 - (6.7 - 5) =40 Step 3: Multiply 11.7 = 77 and 6.7 = 42 77 - (42 - 5) = 40 Step 4: Solve parenthesis 42 - 5 = 37 77 - 37 = 40 Step 5: Subtract 40 = 40 Since the check results in true statement, we conclude that the solution set of the given equation is {7}
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