Question

solve for x and graph the solution.
|x - 5|>4
click to select points on the number line.

Explanation:

Step1: Solve the absolute - value inequality

For \(|x - 5|>4\), we consider two cases.
Case 1: \(x - 5>4\).
Adding 5 to both sides gives \(x>4 + 5\), so \(x>9\).
Case 2: \(-(x - 5)>4\).
First, expand to get \(-x + 5>4\).
Subtract 5 from both sides: \(-x>4 - 5=-1\).
Multiply both sides by - 1 and reverse the inequality sign, we get \(x < 1\).

Step2: Graph on the number - line

On the number - line, we mark an open circle at \(x = 1\) and shade to the left of 1, and mark an open circle at \(x = 9\) and shade to the right of 9.

Answer:

The solution is \(x<1\) or \(x > 9\). On the number - line, open circles at 1 and 9 with shading to the left of 1 and to the right of 9.