Question

solve the inequality |x + 4|≥3
-7≤x≤-1
x≤-7 or x≥-1
1≤x≤7
x≤1 or x≥7
graph the solution.

Explanation:

Step1: Recall absolute - value inequality rule

If \(|u|\geq a\) (\(a>0\)), then \(u\geq a\) or \(u\leq - a\). Here \(u = x + 4\) and \(a = 3\), so \(x+4\geq3\) or \(x + 4\leq-3\).

Step2: Solve \(x+4\geq3\)

Subtract 4 from both sides: \(x+4 - 4\geq3 - 4\), which gives \(x\geq-1\).

Step3: Solve \(x + 4\leq-3\)

Subtract 4 from both sides: \(x+4 - 4\leq-3 - 4\), which gives \(x\leq-7\).

Answer:

\(x\leq - 7\) or \(x\geq - 1\)