Chapter 1.1, Problem 50E

To determine

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

Answer to Problem 50E

In terms of inequality the interval can be expressed as $-\infty <x<1$ .

Explanation of Solution

Given information:

An interval is given as

  $\left(-\infty ,1\right)$

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.

  $\left(-\infty ,1\right)$

Let us consider a variable x o express the inequality.

So, the interval can be expressed as an inequality as $-\infty <x<1$ .

Graph:

Now, graph the interval on number line as shown:

  

Here, $-\infty \text{and}1$ both the points are excluded from the interval, the interval start from $-\infty$ and goes up to 1 so, open ball is placed for $1$ on the number line.