Question

Solve the inequation and represent the solution set on the number line. `-3 + x ≤ (8x)/(3) + 2 ≤ (14)/(3) + 2x, "Where" x ∈ "I"`

Answer 1

Given: `-3 + x ≤ (8x)/(3) + 2 ≤ (14)/(3) + 2x, "Where" x ∈ "I"`

(i) `-3 + x ≤ (8x)/(3) + 2`

`-3 - 2 ≤ (8x)/(3) - x`

⇒ `-5 ≤ (5x)/(3)`

⇒  `-1 ≤ x/(3)`
–3 ≤ x                    ....(i)
and 
`(8x)/(3) - 2x ≤ (14)/(3)`

⇒ `(2x)/(3) ≤ (8)/(3)`
⇒  x ≤ 4                ....(ii)
From (i) and (ii),

⇒ `-5 ≤ (5x)/(3) and (2x)/(3) ≤ (8)/(3)`
⇒  x ≥ –3 and x ≤ 4
∴ –3 ≤ x ≤ 4
Solution set = {–3, -2, –1, 0, 1, 2, 3, 4}
Solution set on number line