Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 3 - Cumulative Review: 25

Answer

$(-∞,-\frac{7}{3}]$

Work Step by Step

We are given that $\frac{2}{5}(x-6)\geq x-1$. To solve for x, first simplify the left side by using the distributive property. $\frac{2}{5}x-\frac{12}{5}\geq x-1$ Add $\frac{12}{5}$ to both sides of the equation. $\frac{2}{5}x\geq x+\frac{7}{5}$ Subtract x from both sides. $-\frac{3}{5}x\geq\frac{7}{5}$ Multiply both sides by 5. $-3x\geq7$. Divide both sides by -3 (which will reverse the inequality sign). $x\leq-\frac{7}{3}$ Therefore, the inequality will be satisfied by all values of x that are less than or equal to $-\frac{7}{3}$.
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