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: 59

Answer

$[2, \infty)$ Refer to the graph below.

Work Step by Step

Add $1$ and subtract $x$ to both sides, then combine like terms to obtain $$ 3x-1+1-x\geq 3+x+1-x \Longrightarrow 2x\gt 1 -5\Longrightarrow 2x\geq 4 .$$ Now, by dividing both sides by $2$, we have $x\geq 2$. In terms of intervals, $x\in [2,\infty)$. To graph, plot a solid dot at $x=2$, then shade the region to its right. See the figure below.
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