Chapter 8.6, Problem 9GP

To determine

Graph the inequality $z\le 2$ on a number line.

Explanation of Solution

Given:

The inequality: $z\le 2$

Concept Used:

To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (= or =), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.

Calculation:

1) Draw a number line. 2) Put either an open circle or a closed dot above the number given. For = and = , use a closed dot to indicate the number itself is part of the solution. For < and >, use an open circle to indicate the number itself is not part of the solution

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( $\ge$ ) or less than or equal to ( $\le$ ). The point is part of the solution.

An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction.

For = and <, the arrow points down to the left.

For = and >, the arrow points up to the right.