Question

Solve the following in equation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R

Answer 1

13x - 5 < 15x + 4 < 7x + 12, x ∈ R

We have

13x - 5 < 15x + 4

`=>13x < 15x + 9`

`=> 0 < 2x + 9`

`=> -9 < 2x`

`=> -9/2 < x`

`∴ -9/2 < x < 1`

i.e -4.5 < x  < 1

and

15x + 4 < 7x + 12

`=> 15x < 7x +  8`

=> 8x  < 8

=> x < 1

=> x < 1

∴ Solution set = {x : x ∈ R and -4.5 < x < 1}

The required line is