Question

Find the values of x, which satisfy the inequation : `-2 ≤ (1)/(2) - (2x)/(3) ≤ 1(5)/(6)`, x ∈ N. Graph the solution set on the number line.

Answer 1

`-2 ≤ (1)/(2) - (2x)/(3) ≤ 1(5)/(6)`, x ∈ N

⇒ `-2 - (1)/(2) ≤ (1)/(2) - (2x)/(3) - (1)/(2) ≤ (11)/(6) - (1)/(2)`

[By subtracting `(1)/(2)` on both sides of inequality]

⇒ `-(5)/(2) ≤ (2x)/(3) ≤ (8)/(6)`
⇒ -15 ≤ - 4x ≤ 8
⇒ 15 ≥ 4x ≥ - 8

⇒ `(15)/(4)` ≥ x ≥ - 2

`3(3)/(4)` ≥ x ≥ - 2
But x ∈ N, hence only possible solution for x = {1, 2, 3}