Question

1. solve for x and graph the solution on the number line below. 3 - x > 2

Explanation:

Step1: Solve the absolute - value inequality

Given \(|x|>3/2\). By the definition of absolute - value, if \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). So \(x>\frac{3}{2}\) or \(x<-\frac{3}{2}\).

Step2: Graph on the number line

On the number line, mark the points \(x =-\frac{3}{2}=-1.5\) and \(x=\frac{3}{2}=1.5\). Use open - circles at \(x = - 1.5\) and \(x = 1.5\) (since the inequality is strict, \(x
eq\pm1.5\)) and shade the regions to the left of \(x=-1.5\) and to the right of \(x = 1.5\).

Answer:

The solution of the inequality is \(x<-\frac{3}{2}\) or \(x>\frac{3}{2}\). On the number line, open - circles are at \(x=-1.5\) and \(x = 1.5\), and the regions to the left of \(x=-1.5\) and to the right of \(x = 1.5\) are shaded.