Question

solve for w and graph the solution.
225 ≥ |-5w - 925|
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: Rewrite absolute - value inequality

The inequality $225\geq|-5w - 925|$ is equivalent to $- 225\leq-5w - 925\leq225$.

Step2: Solve the left - hand side of the compound inequality

Add 925 to all parts: $-225 + 925\leq-5w-925 + 925\leq225 + 925$, which simplifies to $700\leq-5w\leq1150$.

Step3: Divide all parts by - 5 and reverse the inequality signs

When dividing by a negative number, the inequality signs reverse. So $\frac{700}{-5}\geq\frac{-5w}{-5}\geq\frac{1150}{-5}$, resulting in $-140\geq w\geq - 230$.

Answer:

The solution is $-230\leq w\leq - 140$. On the number - line, click on the points at $w=-230$ and $w = - 140$ and make them filled - in circles, then click between them to graph the line segment.