Question

graph your solution to the inequality. |14 - m| > 6

Explanation:

Step1: Split absolute - value inequality

For \(|14 - m|>6\), we have two cases: \(14 - m>6\) or \(14 - m < - 6\).

Step2: Solve the first inequality

Solve \(14 - m>6\). Subtract 14 from both sides: \(-m>6 - 14\), so \(-m>-8\). Multiply both sides by - 1 and reverse the inequality sign, we get \(m < 8\).

Step3: Solve the second inequality

Solve \(14 - m < - 6\). Subtract 14 from both sides: \(-m < - 6-14\), so \(-m < - 20\). Multiply both sides by - 1 and reverse the inequality sign, we get \(m>20\).

Answer:

The solution is \(m < 8\) or \(m>20\). On the number - line, we have an open circle at \(m = 8\) and shade to the left, and an open circle at \(m = 20\) and shade to the right.