Question

graph the solution to the inequality on the number line.
$|v - 8| \leq 2$

Explanation:

Step1: Solve the absolute - value inequality

For \(|v - 8|\leq2\), we use the property \(|x|\leq a\) implies \(-a\leq x\leq a\). Here \(x = v - 8\) and \(a = 2\). So we have \(-2\leq v-8\leq2\).

Step2: Solve the compound inequality for \(v\)

Add 8 to all parts of the compound inequality:
\(-2 + 8\leq v-8 + 8\leq2+8\).
\(6\leq v\leq10\).

Step3: Graph the solution on the number line

On the number line, we draw a closed circle at \(v = 6\) (because \(v\) can be equal to 6) and a closed circle at \(v = 10\) (because \(v\) can be equal to 10), and then connect these two points with a line segment.

Answer:

The solution of the inequality \(|v - 8|\leq2\) is \(6\leq v\leq10\). On the number line, we mark closed - circles at \(6\) and \(10\) and connect them.