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Q36.

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.
$| p + 2 | > 7$

The solution for the given inequality $|p + 2| > 7$ is $p \in (- \infty, - 9) \cup (5, \infty)$ .

The graph of the solution set which is $p \in (- \infty, - 9) \cup (5, \infty)$ is:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Solve the given inequality |p+2|>7.

The solution of the given inequality $|p + 2| > 7$ is:

Case 1: $p + 2$ is non-negative.

$\begin{matrix} p + 2 > 7 \\ p + 2 - 2 > 7 - 2 \\ p > 5 \\ p \in (5, \infty) \end{matrix}$

Case 2: $p + 2$ is negative.

$\begin{matrix} - (p + 2) > 7 \\ (- 1) (- (p + 2)) < (- 1) (7) \\ p + 2 < - 7 \\ p + 2 - 2 < - 7 - 2 \\ p < - 9 \\ p \in (- \infty, - 9) \end{matrix}$

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

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

Find the union of the solutions of the inequalities $p + 2 > 7$ and $p + 2 < - 7$ to find the solution of the inequality $|p + 2| > 7$ .

The union of the solutions of the inequalities $p + 2 > 7$ and $p + 2 < - 7$ is:

$p \in (- \infty, - 9) \cup (5, \infty)$

Therefore, the solution of the inequality $|p + 2| > 7$ is $p \in (- \infty, - 9) \cup (5, \infty)$ .

Step 2. Draw the graph of the solution set which is p∈(−∞,−9)∪(5,∞).

The graph of the solution set which is $p \in (- \infty, - 9) \cup (5, \infty)$ is:

Most popular questions for Math Textbooks

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

The highest score that is on record on a video game is 10,219 points. The lowest score on record is 257 points. Which of the following inequalities best shows the range of scores recorded on the game?

F $x \leq 10, 219$

G $x \geq 257$

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J $257 \leq x \leq 10, 219$

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$9 n - 1 < 10 n$

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The world’s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weigh up to 40 pounds.

Write inequalities to describe the ranges of lengths and weights of male bustards.
Male bustards are usually about four times as heavy females. Write and solve an inequality that describes the range of weights of female bustards.

Jane is saving money to buy a new cell phone that costs no more than $90. So far, she has saved $52. How much more money does Jane need to save?

$38
More than $38
No more than $38
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