Chapter 8.6, Problem 31IP

To determine

Write an inequality for the graph.

Answer to Problem 31IP

  $x\le -1$

  

Explanation of Solution

Given information:

The given interval $(-\infty ,-1]$

Concept used:

If there is a parenthesis $\left(\right)$ on the interval, then we use the strict inequality symbols $<\text{ or}>$

If there is a bracket $\left[\right]$ on the interval, then we use the inequality symbols $\le \text{ or}\ge$

Calculation:

To graph the given interval $(-\infty ,-1]$ on a number line, we will put a closed bracket at $-1$ and move to the left infinitely on the number line. The graph of the interval on the number line is shown below:

  

As the graph moving to left infinitely from $-1$ , so the inequality should be $x\le -1$

Thus the inequality is $x\le -1$