Chapter 1.5, Problem 3E

To determine

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

Answer to Problem 3E

In terms of interval the inequality can be expressed as $\left(-\infty ,2\right)\cup \left[14,\infty \right)$ .

Explanation of Solution

Given information:

An inequality is given as

  $\left\{y|y<2\text{or}y\ge 14\right\}$

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.

  $\left\{y|y<2\text{or}y\ge 14\right\}$

So, the inequality can be expressed as an interval as $\left(-\infty ,2\right)\cup \left[14,\infty \right)$ .

Here, $2$ is not included to the interval and 14 is included in the interval.