Question

Solve the following linear in-equation and graph the solution set on a real number line :

`1/3 (2x - 1) < 1/4 (x + 5) < 1/6 (3x + 4)`, x ∈ R

Answer 1

`1/3 (2x - 1) < 1/4 (x + 5)`

4(2x - 1) < 3 (x + 5)

8x - 4 < 3x +15

8x - 3x < 15 + 4

5x < 19

x < `3  4/5`

and

`1/4 (x + 5) < 1/6 (3x + 4)`

6 (x + 5) < 4 (3x + 4)

6x + 30 < 12 x + 16

6x - 12x < 16 -30

-6x < -14

x > `2 1/3`

Solution set = `[2 1/3 < x < 3 4/5]`