Chapter 2, Problem 5CR

To determine

To graph: the inequality.

Explanation of Solution

Given:

  $-1\ge z$

Calculation:

To graph inequalities, locate the number opposite the variable of the inequality ona number line. If the inequality is either $a\le ora\ge$ , use a closed dot, meaning the number is a solution as well. If the inequality is $a>ora<,$ use an open dot, indicating that the number is not a solution.

From here, shade the line going to the left if the inequality is either $\le or<$ and shade the line going to the right if the inequality is either $\ge or\text{ >}$ .

To have an easier time graphing, switch the variable to the left side. In doing this, invert the inequality symbol as well, making it: $z\le -1$ .

The number opposite the variable is -1, look for this in the number line. Since the inequality is $\le$ , use aclosed dot and shade the line going to the left of -1. Therefore, its graph would look like:

  

Conclusion:

Therefore, the required graph is drawn.