Question

Solve the following inequation and represent the solution set on the number line:

${\displaystyle -3<-\frac{1}{2}-\frac{2x}{3}\le \frac{5}{6},x\in R}$

Answer 1

${\displaystyle -3<-\frac{1}{2}-\frac{2x}{3}\le \frac{5}{6}}$

Multiply by 6, we get

${\displaystyle \Rightarrow -18<-3-4x\le 5}$ 

${\displaystyle \Rightarrow -15<-4x\le 8}$

Dividing by – 4, we get

${\displaystyle \Rightarrow \frac{-15}{-4}>x\ge \frac{8}{-4}}$

${\displaystyle \Rightarrow -2\le x<\frac{15}{4}}$

${\displaystyle \Rightarrow x\in [-2,\frac{15}{4}]}$

The solution set can be represented on a number line as: