Question

solve for u and graph the solution. 150 > 6|u - 455| 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: Isolate the absolute - value expression

Divide both sides of the inequality $150>6|u - 455|$ by 6. We get $\frac{150}{6}>|u - 455|$, which simplifies to $25>|u - 455|$ or $|u - 455|<25$.

Step2: Rewrite the absolute - value inequality as a compound inequality

The inequality $|x|0$) is equivalent to $-a < x < a$. So, $|u - 455|<25$ is equivalent to $-25

Step3: Solve the compound inequality

Add 455 to all parts of the compound inequality: $-25 + 455

Answer:

The solution of the inequality is the open interval $(430,480)$. On the number - line, we click on 430 and 480 and change the endpoints to empty circles.