Chapter 5: Q37. (page 324)

Solve each inequality. Then graph the solution set.
$| 2 c + 3 | \leq 11$

Short Answer

Expert verified

The solution for the given inequality $|2 c + 3| \leq 11$ is $c \in [- 7, 4]$ .

The graph of the solution set which is $c \in [- 7, 4]$ is:

Step by step solution

Step 1. Solve the given inequality |2c+3|≤11.

The solution of the given inequality $|2 c + 3| \leq 11$ is:

Case 1: $2 c + 3$ is non-negative.

$\begin{matrix} 2 c + 3 \leq 11 \\ 2 c + 3 - 3 \leq 11 - 3 \\ 2 c \leq 8 \\ \frac{2 c}{2} \leq \frac{8}{2} \\ c \leq 4 \\ c \in (- \infty, 4] \end{matrix}$

Case 2: $2 c + 3$ is negative.

$\begin{matrix} - (2 c + 3) \leq 11 \\ (- 1) (- (2 c + 3)) \geq (- 1) (11) \\ 2 c + 3 \geq - 11 \\ 2 c + 3 - 3 \geq - 11 - 3 \\ 2 c \geq - 14 \\ \frac{2 c}{2} \geq \frac{- 14}{2} \\ c \geq - 7 \\ c \in [- 7, \infty) \end{matrix}$

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 $2 c + 3 \leq 11$ and $2 c + 3 \geq - 11$ to find the solution of the inequality $|2 c + 3| \leq 11$ .

The intersection of the solutions of the inequalities $2 c + 3 \leq 11$ and $2 c + 3 \geq - 11$ is:

$c \in [- 7, 4]$

Therefore, the solution of the inequality $|2 c + 3| \leq 11$ is $c \in [- 7, 4]$ .

Step 2. Draw the graph of the solution set which is c∈[−7,4].

The graph of the solution set which is $c \in [- 7, 4]$ is:

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Solve each inequality. Then graph the solution set.
$| 2 c + 3 | \leq 11$

Short Answer

Step by step solution

Step 1. Solve the given inequality |2c+3|≤11.

Step 2. Draw the graph of the solution set which is c∈[−7,4].

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Solve each inequality. Then graph the solution set.|2c+3|≤11

Short Answer

Step by step solution

Step 1. Solve the given inequality |2c+3|≤11.

Step 2. Draw the graph of the solution set which is c∈[−7,4].

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Discrete Mathematics

Calculus

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set.
$| 2 c + 3 | \leq 11$