Question

graph the solution to the inequality on the number line. |4v - 10| < 6

Explanation:

Step1: Rewrite absolute - value inequality

If \(|a| 0\)), then \(-b < a < b\). So for \(|4v - 10|<6\), we have \(-6<4v - 10<6\).

Step2: Add 10 to all parts

Adding 10 to each part of the compound - inequality \(-6<4v - 10<6\) gives \(-6 + 10<4v-10 + 10<6 + 10\), which simplifies to \(4<4v<16\).

Step3: Divide by 4

Dividing each part of the inequality \(4<4v<16\) by 4, we get \(\frac{4}{4}<\frac{4v}{4}<\frac{16}{4}\), or \(1 < v<4\).

Answer:

On the number line, use an open - circle at \(v = 1\) and an open - circle at \(v = 4\), and shade the region between them.