Question

solve for t and graph the solution.
-407 < -5|600 - 2t| - 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: Isolate the absolute - value expression

Add \(7\) to both sides of the inequality:
\(-407 + 7\lt-5|600 - 2t|-7 + 7\)
\(-400\lt-5|600 - 2t|\)
Divide both sides by \(- 5\). Remember that when dividing by a negative number, the inequality sign flips:
\(\frac{-400}{-5}\gt\frac{-5|600 - 2t|}{-5}\)
\(80\gt|600 - 2t|\)
Rewrite the absolute - value inequality \(|a|\lt b\) (where \(a = 600 - 2t\) and \(b = 80\)) as a compound inequality: \(-80\lt600 - 2t\lt80\)

Step2: Solve the compound inequality for \(t\)

First, subtract \(600\) from all three parts of the compound inequality:
\(-80-600\lt600 - 2t-600\lt80 - 600\)
\(-680\lt-2t\lt-520\)
Then divide all three parts by \(-2\). Since we are dividing by a negative number, the inequality signs flip:
\(\frac{-680}{-2}\gt\frac{-2t}{-2}\gt\frac{-520}{-2}\)
\(340\gt t\gt260\)

Answer:

The solution of the inequality is \(260\lt t\lt340\). On the number - line, we click on \(260\) (change it to an empty circle) and \(340\) (change it to an empty circle) and then click between them to graph the line segment.