Question

Find the values of x which satisfy the inequation:

`-2 <= 1/2 - (2x)/3 ≤ 1 5/6; x ∈ N`

Graph the solution on the number line.

Answer 1

`-2 <= 1/2 - (2x)/3 ≤ 1 5/6`

`-2 <= 1/2 - (2x)/3 `  and `1/2 - (2x)/3 ≤ 1 5/6`

`-2 <= 1/2 - (2x)/3 `  and `1/2 - (2x)/3 ≤ 11/6`

`-2 <=(3-4x)/6   and (2x)/3 ≤ 11/6 - 1/2`

`-12 <=3-4x   and -(2x)/3 ≤ 8/6`

– 4x ≤ 3 + 12 and – 2x ≤ – 4

`x <= 15/4  and x >= 4/(-2)`

x ≤ 3.75  and x ≥ – 2

Thus, the solution set is {x ∊ N: – 2 ≤ x ≤ 3.75}

Since x ∊ N, the values of x are 1, 2, 3

The solution on number line is given by