Question

graph the inequality on a number line.

1. $r \leq -9$
2. $g > 2.75$
3. $x \geq -3\frac{1}{2}$
4. $z < 1\frac{1}{4}$

Explanation:

Step1: Analyze the inequality \(r\leq - 9\)

For the inequality \(r\leq - 9\), we need to represent all values of \(r\) that are less than or equal to \(-9\) on a number line.

Step2: Mark the point on the number line

First, locate \(-9\) on the number line. Since the inequality is \(\leq\) (less than or equal to), we use a closed circle at \(-9\) to include \(-9\) in the solution set.

Step3: Shade the appropriate region

Then, shade the line to the left of \(-9\) because all numbers less than \(-9\) also satisfy the inequality \(r\leq - 9\).

Answer:

On the number line, place a closed circle at \(-9\) and shade the line to the left of \(-9\).