Question

solve for w and graph the solution.
1 < |w + 7|
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Solve the absolute - value inequality

The inequality \(1\lt|w + 7|\) is equivalent to two separate inequalities:
\(w+7\gt1\) or \(w + 7\lt- 1\).
For \(w+7\gt1\):
Subtract 7 from both sides of the inequality.
\(w+7-7\gt1 - 7\), so \(w\gt-6\).
For \(w + 7\lt-1\):
Subtract 7 from both sides of the inequality.
\(w+7-7\lt-1 - 7\), so \(w\lt-8\).

Step2: Graph the solution

The solution \(w\lt-8\) or \(w\gt-6\) is graphed on the number - line.
For \(w\lt-8\), we have a ray starting at \(-8\) (with an empty circle since \(w=-8\) is not included) and going to the left.
For \(w\gt-6\), we have a ray starting at \(-6\) (with an empty circle since \(w = - 6\) is not included) and going to the right.

Answer:

The solution of the inequality is \(w\lt-8\) or \(w\gt-6\). On the number - line, we have two rays: one starting at \(-8\) (open circle) and going to the left, and another starting at \(-6\) (open circle) and going to the right.