Chapter 1.1, Problem 53E

To determine

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

Answer to Problem 53E

In terms of interval the inequality can be expressed as $\left(-2,1\right]$ .

Explanation of Solution

Given information:

An inequalityis given as

  $-2<x\le 1$

Concept used:

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

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

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

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

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

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

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

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

Calculation:

Consider the given inequality.

  $-2<x\le 1$

So, the inequality can be expressed as aninterval as $\left(-2,1\right]$ .

Graph:

Now, graph the interval on number line as shown:

  

Here, $1$ is included to the interval and $-2$ is excluded from the interval so, closed ball is placed for 1 and open ball for $-2$ on the number line.