Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.10 Internal Notation; Solving Inequalities - A.10 Assess Your Understanding - Page A87: 62

Answer

$(-\infty,5)$ See the figure below.

Work Step by Step

Distribute $-3$ and then add $3$ to both sides to obtain $$ - 3(1-x )\lt 12\Longrightarrow -3+3x \lt 12\\ \Longrightarrow -3+3x+3 \lt 12+3 \Longrightarrow 3x\lt 15 .$$ Dividing both sides by $3$, we get $$ 3x\lt 15 \Longrightarrow x \lt 5 .$$ In terms of intervals, $x\in (-\infty,5)$. To graph, plot a circle at $x=5$ then shade the region to its left. See the figure below.
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