Question

Solve the following inequation, write the solution set and represent it on the number line `-x/3 <= x/2 - 1 1/3 < 1/6, x ∈ R`

Answer 1

The given inequation is `-1/3 <= x/2 - 1  1/3 < 1/6, x ∈ R`

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

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

`(2x + 3x)/6 >= 4/3`

`(5x)/6 >= 4/3`

`5x >= 8`

`x >= 8`

`x >= 8/5`

`x >= 1.6`

and

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

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

`x/2 < (1+8)/6`

`x/2 < 9/6`

`x < 18/6`

x < 3

The solution set is `{x: 1.6 <= x < 3, x ∈ R}`

It can be represented on a number line as follows: