Chapter 5: Q19. (page 325)

Solve each inequality. Then graph the solution set. $| 2 f + 7 | \geq 21$

Short Answer

Expert verified

The solution set of inequality is ${f | f \leq - 14 or f \geq 7}$ .

The solution set on number line is

Step by step solution

Step 1. Write two cases of absolute value inequality.

For solving absolute value inequalities, there are two cases

Case 1- The expression inside the absolute value symbols is nonnegative.

Case 2- The expression inside the absolute value symbols is negative.

Step 2. Write given inequality for case 1 and solve.

According to case 1, $| 2 f + 7 | \geq 21$ is nonnegative.

$\begin{matrix} 2 f + 7 \geq 21 \\ 2 f + 7 - 7 \geq 21 - 7 \\ \frac{2 f}{2} \geq \frac{14}{2} \\ f \geq 7 \end{matrix}$

Step 3. Write given inequality for case 2 and solve.

According to case 2, $| 2 f + 7 | \geq 21$ is negative.

$\begin{matrix} - (2 f + 7) \geq 21 \\ 2 f + 7 \leq - 21 \\ 2 f + 7 - 7 \leq - 21 - 7 \\ \frac{2 f}{2} \leq \frac{- 28}{2} \\ f \leq - 14 \end{matrix}$

Therefore, the solution is $f \geq 7$ or $f \leq - 14$ .

Step 4. Write solution set and graph the solution.

The solution set of given inequality is ${t | f \leq - 14 o r f \geq 7}$ .

Closed circles at 7 and $- 14$ shows these points are included into the solution set.

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Solve each inequality. Then graph the solution set. $| 2 f + 7 | \geq 21$

Short Answer

Step by step solution

Step 1. Write two cases of absolute value inequality.

Step 2. Write given inequality for case 1 and solve.

Step 3. Write given inequality for case 2 and solve.

Step 4. Write solution set and graph the solution.

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Solve each inequality. Then graph the solution set.|2f+7|≥21

Short Answer

Step by step solution

Step 1. Write two cases of absolute value inequality.

Step 2. Write given inequality for case 1 and solve.

Step 3. Write given inequality for case 2 and solve.

Step 4. Write solution set and graph the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Discrete Mathematics

Calculus

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set. $| 2 f + 7 | \geq 21$