Question

Solve the following inequation, write down the solution set and represent it on the number line.

`-3 + x <= 7x/2 + 2 < 8+2x, x∈l`

Answer 1

`-3 + x <= (7x)/2 + 2 < 8 + 2x`

`-3 + x <= (7/2)x + 2 x - (7/2)x <= 2 + 3 -(5/2)x <= 5 => x >= -2`

`(7/2)x + 2 < 8 + 2x (7/2 - 2)x < 6 (3/2)x < 6 => x < 4`

Combine:

`-2 <= x < 4`, i.e. the solution in real numbers is [−2, 4].

If the replacement set is the integers (x ∈ I) the integers:

x ∈ {−2, −1, 0, 1, 2, 3}