Question

Solve the following inequation and write the solution set $13x-5<15x+4<7x+12,x\in R$ . Represent the solution on a number line.

Answer 1

Step 1: Solve the inequation

$$\begin{gathered} 13x-5<15x+4<7x+12 \\ 13x-5<15x+4and15x+4<7x+12 \\ -9<2xand8x<8 \\ x>-4.5andx<1 \end{gathered}$$

Step2: Marking the solution set on the number line

The solution set will be$-4.5<x<1$, so the solution set on the number line will be

Hence the solution set of the inequality $13x-5<15x+4<7x+12,x\in R$ is $-4.5<x<1$ or $\left(-4.5,1\right)$and the representation of the solution set on the number line is as shown above.