Question

solve for v and graph the solution. 75 > |v - 375| click two endpoints to graph a line segment, an endpoint and an arrow, or two arrowheads to graph a line. to change endpoints from filled - in circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| < a\) (where \(a>0\)), the solution is \(-a < x < a\). So for \(75 > |v - 375|\), we can rewrite it as \(|v - 375| < 75\), which means \(-75 < v - 375 < 75\).

Step2: Solve left inequality

Solve \(-75 < v - 375\). Add 375 to both sides: \(-75 + 375 < v\), so \(300 < v\).

Step3: Solve right inequality

Solve \(v - 375 < 75\). Add 375 to both sides: \(v < 75 + 375\), so \(v < 450\).

Step4: Combine solutions

Combining the two inequalities, we get \(300 < v < 450\).

Answer:

The solution for \(v\) is \(300 < v < 450\). To graph this, we would plot an open circle at 300, an open circle at 450, and draw a line segment between them (since the inequality is strict, the endpoints are not included).