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.

Find the values of x, which satisfy the inequation: `-2 5/6 < 1/2 - (2x)/3 <= 2`, x ∈ W

Answer 1

We need to find the values of x, such that x satisfies the inequation `-2 5/6 < 1/2 - (2x)/3 <=2 ∈ W`

Consider the given inequation:

`-2 5/6 < 1/2 - (2x)/3 <= 2, x ∈ W`

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 < 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 values of x are 0, 1, 2, 3, 4

And the required line is