Question

Solve: `-x/3 <= x/2 - 1 1/3 < 1/6`, x ∈ R and represent the solution on the number line.

Answer 1

Compound inequality:

`-x/3 <= x/2 - 1 1/3 < 1/6`

`1 1/3 = 4/3`

`-x/3 <= x/2 - 4/3 < 1/6`

Part 1:

`-x/3 <= x/2 - 4/3`

`-x/3 + 4/3 <= x/2`

−2x + 8 ≤ 3x

8 ≤ 5x

⇒ x ≥ `8/5`

Part 2:

`x/2 - 4/3 < 1/6`

`x/2 < 1/6 + 4/3`

`=1/6+8/6`

`=9/6`

`=3/2`

`x/2<3/2`

⇒ x < 3

`8/5 <= x <= 3`