Chapter 1.1, Problem 48E

To determine

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

Answer to Problem 48E

In terms of inequality the interval can be expressed as $-6\le x\le -\frac{1}{2}$ .

Explanation of Solution

Given information:

An interval is given as

  $\left[-6,-\frac{1}{2}\right]$

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.

  $\left[-6,-\frac{1}{2}\right]$

Let us consider a variable x o express the inequality.

So, the interval can be expressed as an inequality as $-6\le x\le -\frac{1}{2}$ .

Graph:

Now, graph the interval on number line as shown:

  

Here, $-6,-\frac{1}{2}$ both are included to the interval so, closed ball is place for $-6,-\frac{1}{2}$ on the number line.