Chapter 1.1, Problem 46E

To determine

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

Answer to Problem 46E

In terms of inequality the interval can be expressed as $2<x\le 8$ .

Explanation of Solution

Given information:

An interval is given as

  $\left(2,8\right]$

Concept used:

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

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

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

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

Calculation:

Consider the given interval.

  $\left(2,8\right]$

Let us consider a variable x o express the inequality.

So, the interval can be expressed as an inequality as $2<x\le 8$ .

Graph:

Now, graph the interval on number line as shown:

  

Here, $2$ is excluded from the interval and 8 is included to the interval so, open ballis placed for $2$ and closed ball is place for 8 on the number line.