Algebra 2 (1st Edition)

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

Chapter 1, Equations and Inequalities - 1.6 Solve Inequalities - 1.6 Exercises - Skill Practice - Page 45: 31


$x\displaystyle \lt\frac{1}{2}$ Please see image

Work Step by Step

$ 21x+7\lt 3x+16\qquad$ ...add $-3x$ to each side of the inequality. $ 21x+7-3x\lt 3x+16-3x\qquad$ ...simplify. $ 18x+7\lt 16\qquad$ ...add $-7$ to each side of the inequality. $ 18x+7-7\lt 16-7\qquad$ ...simplify. $ 18x\lt 9\qquad$ ...divide with $18$. $ x\displaystyle \lt\frac{9}{18}\qquad$ ...simplify. $x\displaystyle \lt\frac{1}{2}$ The solutions of the given inequality are all real numbers smaller than $\displaystyle \frac{1}{2}$. Smaller numbers are to the left of $\displaystyle \frac{1}{2}$. Use an open dot in the graph to indicate $\displaystyle \frac{1}{2}$ is not a solution.
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