Question

Solve the inequation : `-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`. Graph the solution set on the number line.

Answer 1

`-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`

`-(5)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x`

`-(5)/(2) + 2x ≤ (4x)/(3) and (4x)/(3) ≤ (4)/(3) + 2x`

`2x - (4x)/(3) ≤ (5)/(2) and (4x)/(3) - 2x ≤ (4)/(3)`
12 x - 8x ≤ 15 and 4x - 6x ≤ 4
4x ≤ 15 and -2x ≤ 4

`x ≤ (15)/(4) and -x ≤ 4`

`x ≤ (15)/(4) and x ≥ 4 `

`x ≤ (15)/(4) and  -4 ≤ x `

∴ `-2 ≤ x ≤ (15)/(4)` 
∴ x = 0, 1, 2, 3
Solution set {x : x ∈ W, x ≤ 3}
Solution set on number line