Question

Solve the following inequation and write the solution set:

13x – 5 < 15x + 4 < 7x + 12, x ∈ R

Represent the solution on a real number line.

Answer 1

13x – 5 < 15x + 4 < 7x + 12, x ∈ R

Take 13x – 5 < 15x + 4 

13x < 15x + 9

0 < 2x + 9

– 9 < 2x

`-9/2 < x`

and

15x + 4 < 7x + 12

15x < 7x + 8

8x < 8

x < 1

∴ `-9/2 < x < 1`

i.e – 4.5 < x < 1

∴ Solution set = {x: – 4.5 < x < 1, x ∈ R}

The solution on the number line is as follows: