Question

solve for y and graph the solution.
35 ≤ |y + 735|
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: Recall absolute - value inequality rule

If \(a\leq|x|\), then \(x\leq - a\) or \(x\geq a\). Here \(a = 35\) and \(x=y + 735\), so \(y+735\leq - 35\) or \(y + 735\geq35\).

Step2: Solve the first inequality \(y+735\leq - 35\)

Subtract 735 from both sides: \(y\leq-35 - 735\), so \(y\leq - 770\).

Step3: Solve the second inequality \(y + 735\geq35\)

Subtract 735 from both sides: \(y\geq35 - 735\), so \(y\geq - 700\).

Answer:

The solution is \(y\leq - 770\) or \(y\geq - 700\). On the number - line, for \(y\leq - 770\), click on \(-770\) (filled - in circle) and an arrowhead to the left. For \(y\geq - 700\), click on \(-700\) (filled - in circle) and an arrowhead to the right.