Question

graph the solution to the inequality on the number line.
|x + 2| ≤ 8
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Explanation:

Step1: Remove absolute - value

We know that if \(|a|\leq b\) (\(b\geq0\)), then \(-b\leq a\leq b\). So for \(|x + 2|\leq8\), we have \(-8\leq x+2\leq8\).

Step2: Solve for \(x\)

Subtract 2 from all parts of the compound - inequality: \(-8-2\leq x+2 - 2\leq8 - 2\), which simplifies to \(-10\leq x\leq6\).

Step3: Graph on number line

On the number line, we use a closed - circle at \(x=-10\) and \(x = 6\) (because the inequality includes equality, \(\leq\)) and draw a line segment connecting them.

Answer:

On the number line, place a closed - circle at \(-10\) and a closed - circle at \(6\), and draw a line segment between them.