Chapter 5: Q41. (page 280)

Solve each inequality. Then graph the solution set. $| \frac{2 t + 6}{2} | > 10$

Short Answer

Expert verified

The solution set of inequality is ${t | t < - 13 o r t > 7}$ .

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, $| \frac{2 t + 6}{2} | > 10$ is nonnegative.

$\begin{matrix} \frac{2 t + 6}{2} > 10 \\ 2 (\frac{2 t + 6}{2}) > 2 (10) \\ 2 t + 6 - 6 > 20 - 6 \\ \frac{2 t}{2} > \frac{14}{2} \\ t > 7 \end{matrix}$

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

According to case 2, $| \frac{2 t + 6}{2} | > 10$ is negative.

$\begin{matrix} - (\frac{2 t + 6}{2}) > 10 \\ 2 (\frac{2 t + 6}{2}) < - 2 (10) \\ 2 t + 6 - 6 < - 20 - 6 \\ \frac{2 t}{2} < \frac{- 26}{2} \\ t < - 13 \end{matrix}$

Therefore, the solution is $t < - 13$ or $t < - 13$ .

Step 4. Write solution set and graph the solution.

The solution set of given inequality is ${t | t < - 13 o r t > 7}$ .

Open circles at 7 and $- 13$ shows these points are excluded from the solution set.

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Solve each inequality. Then graph the solution set. $| \frac{2 t + 6}{2} | > 10$

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.|2t+62|>10

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

Probability and Statistics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set. $| \frac{2 t + 6}{2} | > 10$