Question

solve the inequality. graph the solution. |x + 15| > 7

Explanation:

Step1: Split into two inequalities

If \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). So for \(|x + 15|>7\), we have \(x+15>7\) or \(x + 15<-7\).

Step2: Solve \(x+15>7\)

Subtract 15 from both sides: \(x+15 - 15>7 - 15\), which simplifies to \(x>-8\).

Step3: Solve \(x + 15<-7\)

Subtract 15 from both sides: \(x+15-15<-7 - 15\), which simplifies to \(x<-22\).

Answer:

The solution is \(x < - 22\) or \(x>-8\). To graph, draw an open - circle at \(x=-22\) and shade to the left, and draw an open - circle at \(x = - 8\) and shade to the right on the number line.