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Q42.

Expert-verified

Algebra 1

Found in: Page 324

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

Solve each inequality. Then graph the solution set.
$| - 4 y - 3 | < 13$

The solution for the given inequality $|- 4 y - 3| < 13$ is $y \in (- 4, 2 .5)$ .

The graph of the solution set which is $y \in (- 4, 2.5)$ is:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Solve the given inequality |−4y−3|<13.

The solution of the given inequality $|- 4 y - 3| < 13$ is:

Case 1: $- 4 y - 3$ is non-negative.

$\begin{matrix} - 4 y - 3 < 13 \\ - 4 y - 3 + 3 < 13 + 3 \\ - 4 y < 16 \\ \frac{- 4 y}{- 4} > \frac{16}{- 4} \\ y > - 4 \\ y \in (- 4, \infty) \end{matrix}$

Case 2: $- 4 y - 3$ is negative.

$\begin{matrix} - (- 4 y - 3) < 13 \\ (- 1) (- (- 4 y - 3)) > (- 1) (13) \\ - 4 y - 3 > - 13 \\ - 4 y - 3 + 3 > - 13 + 3 \\ - 4 y > - 10 \\ \frac{- 4 y}{- 4} < \frac{- 10}{- 4} \\ y < \frac{5}{2} \\ y < 2.5 \\ y \in (- \infty, 2.5) \end{matrix}$

The solution of the inequality $|x| \leq a$ is $x \geq - a$ and $x \leq a$ .

That implies the solution of the inequality $|x| \leq a$ is the intersection of the solutions of the inequalities $x \geq - a$ and $x \leq a$ .

Find the intersection of the solutions of the inequalities $- 4 y - 3 < 13$ and $- 4 y - 3 > - 13$ to find the solution of the inequality $|- 4 y - 3| < 13$ .

The intersection of the solutions of the inequalities $- 4 y - 3 < 13$ and $- 4 y - 3 > - 13$ is:

$y \in (- 4, 2.5)$

Therefore, the solution of the inequality $|- 4 y - 3| < 13$ is $y \in (- 4, 2.5)$ .

Step 2. Draw the graph of the solution set which is y∈(−4,2.5).

The graph of the solution set which is $y \in (- 4, 2.5)$ is:

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