Question

graph the solution to the inequality on the number line.
$|x - 3| \leq 3$

Explanation:

Step1: Solve the absolute - value inequality

For \(|x - 3|\leq3\), we use the property \(|a|\leq b\) (where \(b\geq0\)) which is equivalent to \(-b\leq a\leq b\). So, \(- 3\leq x - 3\leq3\).

Step2: Add 3 to all parts of the compound inequality

Adding 3 to each part: \(-3 + 3\leq x-3 + 3\leq3 + 3\).
This simplifies to \(0\leq x\leq6\).

Step3: Graph on the number - line

On the number - line, we draw a closed circle at \(x = 0\) (because \(x\) can be equal to \(0\)) and a closed circle at \(x = 6\) (because \(x\) can be equal to \(6\)), and then connect the two points with a solid line segment.

Answer:

The solution of the inequality \(|x - 3|\leq3\) is \(0\leq x\leq6\). On the number - line, we mark closed circles at \(0\) and \(6\) and draw a solid line segment between them.