Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Appendix A - Equations and Inequalities: 81

Answer

$[-1,\infty)$

Work Step by Step

Step 1: $-2x-2\leq1+x$ Step 2: Adding $2$ to both sides, $-2x-2+2\leq1+x+2$ Step 3: $-2x\leq3+x$ Step 4: Subtracting $x$ from both sides, $-2x-x\leq3+x-x$ Step 5: $-3x\leq3$ Step 6: Dividing both sides by -3 (this reverses the direction of the inequality symbol): $\frac{-3x}{-3} \geq \frac{3}{-3}$ Step 5: $x\geq-1$ According to the inequality, the interval includes $-1$ and all values greater than $-1$. Since $-1$ is part of the interval, a square bracket is used on its side. On the other hand, we represent all values greater than $-1$ by the symbol $\infty$. Therefore, a parenthesis is used on its side. Therefore, the interval notation for this inequality is written as $[-1,\infty)$.
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