Question

graph the solution to the inequality on the number line.
|v| ≤ 7
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Explanation:

Step1: Solve the absolute - value inequality

The absolute - value inequality \(|v|\leq7\) can be rewritten as a compound inequality. By the definition of absolute value, if \(|x|\leq a\) (where \(a\geq0\)), then \(-a\leq x\leq a\). So for \(|v|\leq7\), we have \(- 7\leq v\leq7\).

Step2: Graph the solution on the number line

• First, we look at the endpoints. Since the inequality is "less than or equal to", we use closed circles (filled - in circles) at \(v = - 7\) and \(v=7\) to indicate that these points are included in the solution set.
• Then, we shade the region between \(-7\) and \(7\) on the number line. This region includes all real numbers \(v\) such that \(-7\leq v\leq7\).

Answer:

To graph \(|v|\leq7\) (which is equivalent to \(-7\leq v\leq7\)) on the given number line:

1. Place a closed circle (filled circle) at \(-7\) and at \(7\) on the number line.
2. Shade the region between \(-7\) and \(7\) (including the points \(-7\) and \(7\)).