Question

setup, solve and graph. provide answers accurate to the nearest tenth.
|-x + 2| ≤ 8
write the inequality as a compound inequality. do not solve or simplify
the inequality yet.
solution
graph
number line options

Explanation:

Step1: Recall the property of absolute - value inequalities

For \(|u|\leq a\) (\(a\geq0\)), the compound inequality is \(-a\leq u\leq a\). Here \(u=-x + 2\) and \(a = 8\).
So the compound inequality is \(-8\leq -x+2\leq8\).

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

First, subtract 2 from all parts of the compound inequality:
\(-8-2\leq -x+2 - 2\leq8 - 2\), which simplifies to \(-10\leq -x\leq6\).
Then multiply all parts by \(- 1\). When multiplying by a negative number, the direction of the inequality signs changes. So we get \(10\geq x\geq - 6\) or \(-6\leq x\leq10\).

Answer:

• Compound inequality: \(-8\leq -x + 2\leq8\)
• Solution: \(-6\leq x\leq10\)
• Graph: On a number line, draw a solid circle at \(x=-6\) and \(x = 10\) and shade the region between them.