Chapter 2: Q. 2.145 (page 204)

Graph the solution and write the solution in interval notation: $| x | < 9$

Short Answer

Expert verified

The solution of the inequality is $(- 9, 9)$ .

The graph of the solution is shown below:

Step by step solution

Step 1. Given Information.

We have:

$|x| < 9$

Step 2. Write the equivalent inequality and draw into the number line.

$|x| < 9$

Apply absolute rule: $If | u | < a, a > 0 then - a < u < a$

$- 9 < x < 9$

Step 3. Draw the solution on the number line.

Draw solution $- 9 < x < 9$ on the number line:

Interval notation: $(- 9, 9)$

Step 4. Check each solution.

To verify, check a value in each section of the number line showing the solution. Choose numbers such as $- 10, 1,$ and $10 .$

$| x | < 9$

$| - 10 | < 9 10 < 9$

False.

$| x | < 9 |1| < 9$

True.

$| x | < 9 | 10 | < 9$

True.

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Graph the solution and write the solution in interval notation: $| x | < 9$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the equivalent inequality and draw into the number line.

Step 3. Draw the solution on the number line.

Step 4. Check each solution.

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Graph the solution and write the solution in interval notation:|x|<9

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the equivalent inequality and draw into the number line.

Step 3. Draw the solution on the number line.

Step 4. Check each solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Logic and Functions

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Graph the solution and write the solution in interval notation: $| x | < 9$