Question

5 graph your solution to the inequality. |2s - 7| < 1

Explanation:

Step1: Rewrite absolute - value inequality

The inequality \(|2s - 7|\lt1\) can be rewritten as \(- 1\lt2s - 7\lt1\).

Step2: Add 7 to all parts

Adding 7 to each part of \(-1\lt2s - 7\lt1\) gives \(-1 + 7\lt2s-7 + 7\lt1 + 7\), which simplifies to \(6\lt2s\lt8\).

Step3: Divide by 2

Dividing each part of \(6\lt2s\lt8\) by 2 gives \(\frac{6}{2}\lt\frac{2s}{2}\lt\frac{8}{2}\), or \(3\lt s\lt4\).

Answer:

On the number - line, we use an open circle at \(s = 3\) and an open circle at \(s = 4\), and shade the region between them.