Question

solve for y and graph the solution. 225 ≥ |3y + 225| click two endpoints to graph a line - segment, an endpoint and an arrow - head to graph a ray, or two arrow - heads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Rewrite absolute - value inequality

We know that if \(a\geq|x|\), then \(-a\leq x\leq a\). So for \(225\geq|3y + 225|\), we have \(-225\leq3y + 225\leq225\).

Step2: Solve the left - hand side of the compound inequality

Subtract 225 from all parts: \(-225-225\leq3y+225 - 225\leq225 - 225\), which simplifies to \(-450\leq3y\leq0\).

Step3: Solve for y

Divide all parts by 3: \(\frac{-450}{3}\leq\frac{3y}{3}\leq\frac{0}{3}\), so \(-150\leq y\leq0\).

Answer:

The solution for \(y\) is \(-150\leq y\leq0\). To graph, click on the points at \(y=-150\) and \(y = 0\) and make them filled - in circles, then click between them to form a line segment.