Question

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

`-3 <= 1/2 - (2 "x")/3 <= 2 2/3` , x  ∈ N

Answer 1

`-3 <= 1/2 - (2 "x")/3`

`-3 <= (3 - 4 "x")/6`

-18 ≤ 3 - 4x

-18 - 3 ≤ - 4x

-21 ≤ - 4x

x ≤ `21/4`

x ≤  `5 1/4`

and 

`1/2 - (2 "x")/3 <= 2 2/3`

`(3 - 4 "x")/6 <= 8/3`

9 - 12x ≤ 48

-12 x ≤ 39

12 x ≥ - 39

x ≥ `-3 1/4`

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