Question

Solve the following inequation and graph the solution on the number line.
`-2(2)/(3) ≤ x + (1)/(3) < 3(1)/(3); x ∈ "R"`

Answer 1

The given inequation has two parts:
`-2(2)/(3) ≤ x + (1)/(3) and x + (1)/(3) < 3 (1)/(3)`

`-(8)/(3) ≤ x + (1)/(3) and x + (1)/(3) < (10)/(3)`

`-(8)/(3) - (1)/(3) ≤ x and x < (10)/(3) - (1)/(3)`

`-(9)/(3) ≤ x and x ≤ (9)/(3)`
-3 ≤ x and x < 3
-3 ≤ x < 3
∴ The required graph line is: