Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 56: 40

Answer

B

Work Step by Step

An equation with an absolute value in it is equivalent to two equations together, in this case, $|3x+7|=5x$ is equivalent to $3x+7=5x$ and $3x+7=-5x$. Solve for x in each equation: I) $3x+7=5x$ Subtract 3x from each side: $7=5x-3x$ $7=(5-3)x$ $7=2x$ Divide both sides by 2: $x=\frac72$ II) $3x+7=-5x$ Subtract 3x from each side: $7=-5x-3x$ $7=(-5-3)x$ $7=-8x$ Divide both sides by -8: $x=-\frac78$ The two solutions for this equation are then $-\frac78$ and $\frac72$, so the correct option is B.
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