Question

solve for y and graph the solution. |y - 6| ≤ 2 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: Solve the absolute - value inequality

For \(|y - 6|\leq2\), we use the property \(|x|\leq a\Rightarrow - a\leq x\leq a\). Here \(x=y - 6\) and \(a = 2\). So, \(-2\leq y-6\leq2\).
Add \(6\) to all parts of the compound inequality: \(-2 + 6\leq y-6 + 6\leq2+6\).

Step2: Simplify the inequality

\(4\leq y\leq8\)

To graph \(4\leq y\leq8\) on the number - line:

• Place a filled - in circle at \(y = 4\) (since \(y\) can be equal to \(4\)) and a filled - in circle at \(y = 8\) (since \(y\) can be equal to \(8\)).
• Then draw a line segment connecting these two points.

Answer:

The solution of the inequality \(|y - 6|\leq2\) is \(4\leq y\leq8\). On the number - line, we have a line segment with filled - in endpoints at \(4\) and \(8\).