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

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 53E
To determine

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

Expert Solution

In terms of interval the inequality can be expressed as (2,1] .

### Explanation of Solution

Given information:

An inequalityis given as

2<x1

Concept used:

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

Aninequality axb in terms of an interval can be expressed as [a,b] .

Aninequality ax<b in terms of an interval can be expressed as [a,b) .

Aninequality a<xb in terms of an interval can be expressed as (a,b] .

Aninequality xb in terms of an interval can be expressed as (,b] .

Aninequality x<b in terms of an interval can be expressed as (,b) .

Aninequality xa in terms of an interval can be expressed as [a,) .

Aninequality x>a in terms of an interval can be expressed as (a,) .

Calculation:

Consider the given inequality.

2<x1

So, the inequality can be expressed as aninterval as (2,1] .

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.

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