Q. 18 PT Solve each inequality. Then grap... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 5: Q. 18 PT (page 325)

Solve each inequality. Then graph the solution set.
$| p 鈭� 5 | < 3$

Short Answer

Expert verified

The solution for the given inequality $|p 鈭� 5| < 3$ is $p 鈭� (2, 8)$ .

The graph of the solution set which is $p 鈭� (2, 8)$ is:

Step by step solution

Step 1. Solve the given inequality |p−5|<3.

The solution of the given inequality $|p 鈭� 5| < 3$ is:

Case 1: $p 鈭� 5$ is non-negative.

$\begin{matrix} p 鈭� 5 < 3 \\ p 鈭� 5 + 5 < 3 + 5 \\ p < 8 \\ p 鈭� (鈭� 鈭�, 8) \end{matrix}$

Case 2: $p 鈭� 5$ is negative.

$\begin{matrix} 鈭� (p 鈭� 5) < 3 \\ (鈭� 1) (鈭� (p 鈭� 5)) > (鈭� 1) (3) \\ p 鈭� 5 > 鈭� 3 \\ p 鈭� 5 + 5 > 鈭� 3 + 5 \\ p > 2 \\ p 鈭� (2, 鈭�) \end{matrix}$

The solution of the inequality $|x| 鈮� a$ is $x 鈮� 鈭� a$ and $x 鈮� a$ .

That implies the solution of the inequality $|x| 鈮� a$ is the intersection of the solutions of the inequalities $x 鈮� 鈭� a$ and $x 鈮� a$ .

Find the intersection of the solutions of the inequalities $p 鈭� 5 < 3$ and $p 鈭� 5 > 鈭� 3$ to find the solution of the inequality $|p 鈭� 5| < 3$ .

The intersection of the solutions of the inequalities $p 鈭� 5 < 3$ and $p 鈭� 5 > 鈭� 3$ is:

$p 鈭� (2, 8)$

Therefore, the solution of the inequality $|p 鈭� 5| < 3$ is $p 鈭� (2, 8)$ .

Step 2. Draw the graph of the solution set which is p∈(2,8).

The graph of the solution set which is $p 鈭� (2, 8)$ is:

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91影视

Solve each inequality. Then graph the solution set.
$| p 鈭� 5 | < 3$

Short Answer

Step by step solution

Step 1. Solve the given inequality |p−5|<3.

Step 2. Draw the graph of the solution set which is p∈(2,8).

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91影视

Solve each inequality. Then graph the solution set.|p鈭�5|<3

Short Answer

Step by step solution

Step 1. Solve the given inequality |p−5|<3.

Step 2. Draw the graph of the solution set which is p∈(2,8).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Calculus

Decision Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set.
$| p 鈭� 5 | < 3$