Question

solve for s and graph the solution.
-7 < -3|1 - s| - 4
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 \(4\) to all parts of the inequality \(-7\lt - 3|1 - s|-4\).
\(-7 + 4\lt-3|1 - s|-4 + 4\)
\(-3\lt-3|1 - s|\)
Divide all parts by \(-3\). Remember that when dividing by a negative number, the inequality sign flips.
\(\frac{-3}{-3}\gt\frac{-3|1 - s|}{-3}\)
\(1\gt|1 - s|\)

Step2: Rewrite the absolute - value inequality

If \(|a|\lt b\) (\(b\gt0\)), then \(-b\lt a\lt b\). Here \(a=(1 - s)\) and \(b = 1\).
\(-1\lt1 - s\lt1\)

Step3: Solve for \(s\)

Subtract \(1\) from all parts of the compound inequality.
\(-1-1\lt1 - s-1\lt1 - 1\)
\(-2\lt - s\lt0\)
Multiply all parts by \(-1\). When multiplying by a negative number, the inequality sign flips.
\(2\gt s\gt0\) or \(0\lt s\lt2\)

Answer:

The solution of the inequality is \(0\lt s\lt2\). On the number - line, we click on \(0\) (change it to an empty circle) and \(2\) (change it to an empty circle) and then click between them to graph the line segment.