Question

Find the range of values of x, which satisfy:

`- 1/3 <= x/2 + 1 2/3 < 5 1/6`

Graph in each of the following cases the values of x on the different real number lines:

1. x ∈ W
2. x ∈ Z
3. x ∈ R

Answer 1

`-1/3 <= x/2 + 1 2/3 < 5 1/6`

`-1/3 - 5/3 <= x/2 < 31/6- 5/3`

`-6/3 <= x/2 < 21/6`

– 4 ≤ x < 7

1. If x ∈ W, range of values of x is {0, 1, 2, 3, 4, 5, 6}

2. If x ∈ Z, the range of values of x is {– 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6}

3. If x ∈ R, range of values of x is – 4 ≤ x < 7