Chapter 2: Q. 2.150 (page 205)

Solve $|x| > 1$ . Graph the solution and write the solution in interval notation.

Short Answer

Expert verified

The solution of the inequality is $x < - 1$ or $x > 1$ .

Interval notation: $(- \infty, - 1) \cup (1, \infty)$

The graph on the number line is:

Step by step solution

Step 1. Write the equivalent inequality.

We have:

$| x | > 1$

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

$x < - 1 or x > 1$

Step 2. Graph the solution.

Plot the point $- 1$ on the number line with an open circle since it is not included in the inequality. Plot the point $1$ on the number line with open circle since it is not included in the inequality.

Draw on the number line:

Step 3. Check the solution.

To verify, check the value in each section of the number line showing the solution. Choose the number such as $- 2, 0,$ and $3 .$

$|x| > 1 |- 2| > 1 2 > 1$

True.

$|x| > 1 |0| > 1 0 > 1$

False.

$|x| > 1 |3| > 1 3 > 1$

True.

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Solve $|x| > 1$ . Graph the solution and write the solution in interval notation.

Short Answer

Step by step solution

Step 1. Write the equivalent inequality.

Step 2. Graph the solution.

Step 3. Check the solution.

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Solvex>1. Graph the solution and write the solution in interval notation.

Short Answer

Step by step solution

Step 1. Write the equivalent inequality.

Step 2. Graph the solution.

Step 3. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Geometry

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve $|x| > 1$ . Graph the solution and write the solution in interval notation.