Question

Give that x ∈ I. Solve the inequation and graph the solution on the number line:
`3≥(x  - 4)/(2)+x/(3)≥2`

Answer 1

`3≥(x  - 4)/(2)+x/(3)≥2`
⇒ `3≥(3(x  - 4)+2x)/(6)≥2`
⇒ 18 ≥ 5x - 12 ≥ 12
⇒ 30 ≥ 5x ≥ 24
⇒ `(24)/(5) ≤ x ≤ 6`           ...(x ∈ I)

∴ The solution set = (5, 6)