Chapter 1: Q26. (page 44)

Write an absolute value inequality for each graph
26.

Short Answer

Expert verified

Absolute value inequality is $|x - 1| \leq 3$

Step by step solution

- Definition of absolute value inequality

For real numbers $a and b$ with b>0

Absolute value inequality is $|a| < b$ when $- b < a and a < b$ , and

Absolute value inequality is $|a| > b$ when $a < - b or a > b$

- Observation from image

From image, solution is all real greater than or equal to -2 and less than or equal to 4

- Write absolute value inequality

Let the real number be x

As $x \geq - 2 and x \leq 4$

Since, subtracting same number on both sides does not change the sign of inequality

Subtract 1 on both sides

$\begin{matrix} x - 1 \geq - 2 - 1 and x - 1 \leq 4 - 1 \\ x - 1 \geq - 3 and x - 1 \leq 3 \end{matrix}$

So from definition, absolute value inequality is

$| x - 1 | \leq 3$

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Write an absolute value inequality for each graph
26.

Short Answer

Step by step solution

- Definition of absolute value inequality

- Observation from image

- Write absolute value inequality

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Write an absolute value inequality for each graph26.

Short Answer

Step by step solution

- Definition of absolute value inequality

- Observation from image

- Write absolute value inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Write an absolute value inequality for each graph
26.