Question

solve for y and graph the solution.
|y - 49| - 2 < 0
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

Add \(2\) to both sides of the inequality \(|y - 49|-2\lt0\).
\(|y - 49|\lt2\)

Step2: Apply the absolute - value inequality rule

If \(|u|\lt a\) (\(a\gt0\)), then \(-a\lt u\lt a\). Here \(u = y - 49\) and \(a = 2\).
\(- 2\lt y-49\lt2\)

Step3: Solve for \(y\)

Add \(49\) to all parts of the compound inequality.
\(-2 + 49\lt y-49 + 49\lt2+49\)
\(47\lt y\lt51\)

Answer:

The solution of the inequality \(|y - 49|-2\lt0\) is \(47\lt y\lt51\). On the number - line, we click on \(47\) (as an empty circle) and \(51\) (as an empty circle) to graph the line segment between them.