Chapter 1.5, Problem 4E

To determine

To express: the given inequality in terms of an interval.

Answer to Problem 4E

In terms of interval the inequality can be expressed as $\left(-\infty ,-9\right]\cup \left(1,\infty \right)$ .

Explanation of Solution

Given information:

An inequality is given as

  $\left\{b|b\le -9\text{or}b>1\right\}$

Concept used:

An inequality $a<x<b$ in terms of an interval can be expressed as $\left(a,b\right)$ .

An inequality $a\le x\le b$ in terms of an interval can be expressed as $\left[a,b\right]$ .

An inequality $a\le x<b$ in terms of an interval can be expressed as $\left[a,b\right)$ .

An inequality $a<x\le b$ in terms of an interval can be expressed as $\left(a,b\right]$ .

An inequality $x\le b$ in terms of an interval can be expressed as $\left(-\infty ,b\right]$ .

An inequality $x<b$ in terms of an interval can be expressed as $\left(-\infty ,b\right)$ .

An inequality $x\ge a$ in terms of an interval can be expressed as $\left[a,\infty \right)$ .

An inequality $x>a$ in terms of an interval can be expressed as $\left(a,\infty \right)$ .

Calculation:

Consider the given inequality.

  $\left\{b|b\le -9\text{or}b>1\right\}$

So, the inequality can be expressed as an interval as $\left(-\infty ,-9\right]\cup \left(1,\infty \right)$ .

Here, $1$ is not included to the interval and $-9$ is included in the interval.