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: 78

Answer

x = $\frac{4}{3}$ Or, using set notation. {x|x = $\frac{4}{3}$}

Work Step by Step

2 + 3(2x - 7) = 9 - 4(3x + 1) First, use the distributive property as needed: 2 + 6x - 21 = 9 - 12x - 4 Next, combine like terms on each side of the equation. You may want to regroup (on each side of the equation) the terms so that like terms are together. Remember, the sign to the left of a term stays with the term. 2 - 21 + 6x = 9 - 4 - 12x -19 + 6x = 5 - 12x Now, add 12x to both sides of the equation. -19 + 6x + 12x = 5 - 12x + 12x -19 + 18x = 5 (completing the addition) Next, add 19 to both sides of the equation. -19 + 19 + 18x = 5 + 19 18x = 24 Last, divide both sides by 18. $\frac{18x}{18}$ = $\frac{24}{18}$ Completing the division we get: x = $\frac{24}{18}$ = $\frac{4}{3}$ (in reduced form.)
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