Question

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

Answer 1

Consider the given inequation:

`-2 5/6 < 1/2 - (2x)/3 ≤ 2`

`=> (-17)/6 < (3 - 4x)/6 < 12/6`

`=> 17/6 > (4x - 3)/6 ≥ (-12)/6`

`=> 17 > 4x - 3 ≥ -12`

`=> -12 ≤ 4x - 3 < 17`

`=> -12 + 3 ≤ 4x - 3 + 3 < 17 + 3`

`=> -9 ≤ 4x < 20`

`=> -9/4 ≤ (4x)/4 < 20/4`

`=> -9/4 ≤ x < 5`

Since x ∈ W, the required solution set = {0, 1 ,2, 3, 4}

And the required number line is as follows: