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Chapter 4: Q56. (page 181)

Write an absolute value inequality for each graph.

Short Answer

Expert verified

Absolute value inequality is $|x + 1| > 2$

Step by step solution

01

- 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 $a < - b or a > b$

02

- Observation from image

From image, solution is all real less than $- 3$ or greater than 1

03

- Write absolute value inequality

Let the real number be x

As $x < - 3 or x > 1$

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

Add 1 on both sides

\begin{matrix} x + 1 < - 3 + 1 or x + 1 > 1 + 1 \\ x + 1 < - 2 or x + 1 > 2 \end{matrix}

So from definition, absolute value inequality is

$|x + 1| > 2$

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Most popular questions from this chapter

Describe the conditions under which matrices can be added or subtracted.

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Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

25. $D - B$

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