Question

graph the solution set for |x| > 3.
number line image
part 4 of 5
(c) the solution set for |x| < 3 is (-3, 3).
part: 4 / 5
part 5 of 5
graph the solution set for |x| < 3.
number line image with tools

Explanation:

Step1: Recall absolute value inequality

The inequality \(|x| < 3\) means the distance of \(x\) from 0 on the number line is less than 3. So, \(x\) is greater than -3 and less than 3, i.e., \(-3 < x < 3\).

Step2: Determine the graph style

For strict inequalities (\(<\) or \(>\)), we use open circles (parentheses) at the endpoints. So, we place open circles at -3 and 3 on the number line.

Step3: Shade the region

Shade the region between -3 and 3 on the number line, as that represents all \(x\) values satisfying \(-3 < x < 3\).

To graph it:

1. Locate -3 and 3 on the number line.
2. Draw open circles (since the inequality is strict, \(x\) cannot be equal to -3 or 3) at -3 and 3.
3. Draw a line segment (or shade) between the open circles at -3 and 3 to represent all \(x\) such that \(-3 < x < 3\).

Answer:

To graph \(|x| < 3\):

• Place open circles (parentheses) at \(x = -3\) and \(x = 3\) on the number line.
• Shade the region between \(-3\) and \(3\) (the interval \((-3, 3)\)) on the number line.