Question

graph the solution to the inequality on the number line.
$|y + 2|\geq2$

Explanation:

Step1: Solve the inequality

For \(|y + 2|\geq2\), we have two cases:
Case 1: \(y+2\geq2\)
Subtract 2 from both sides: \(y+2 - 2\geq2 - 2\), so \(y\geq0\)
Case 2: \(y + 2\leq- 2\)
Subtract 2 from both sides: \(y+2-2\leq-2 - 2\), so \(y\leq - 4\)

Step2: Graph on the number line

For \(y\geq0\), we draw a closed circle at \(0\) (since the inequality is \(\geq\)) and shade to the right.
For \(y\leq - 4\), we draw a closed circle at \(-4\) (since the inequality is \(\leq\)) and shade to the left.

Answer:

The solution is \(y\leq - 4\) or \(y\geq0\). On the number - line, we have a closed circle at \(-4\) with shading to the left and a closed circle at \(0\) with shading to the right.