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

`-x/(3) ≤ x/(2) - 1(1)/(3) < (1)/(6), x ∈ "R"`

`-x/(3) ≤ x/(2) -1(1)/(3)`

`-x/(3) ≤ x/(2) - (4)/(3)`

`(4)/(3) ≤ x/(2) + x/(3)`

`(4)/(3) ≤  (5x)/(6)`

`(6)/(5) xx (4)/(3) ≤  x`

`(8)/(5) ≤ x`

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

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

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

`x < (9 xx 2)/(6)`

x < 3

From (1) and (2)

`(8)/(5) ≤ x < 3`

or 1.6 ≤ x < 3

∴ Solution set {x : 1.6 ≤ x < 3, x ∈ R}