Question

current skill $ 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: Apply absolute - value inequality rule

For \(|A|\leq B\) (\(B\geq0\)), it is equivalent to \(-B\leq A\leq B\). Here \(A=-x + 2\) and \(B = 8\), so \(-8\leq -x+2\leq8\).

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

Subtract \(2\) from all parts: \(-8 - 2\leq -x+2 - 2\leq8 - 2\), which gives \(-10\leq -x\leq6\).
Multiply all parts by \(- 1\) (and reverse the inequality signs): \(10\geq x\geq - 6\) 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 \(-6\) and \(10\) (since the inequality includes equality) and shade the region between them.