Question

Solve the following inequation and represent the solution set on a number line.

`-8 1/2 < -1/2 -4x <= 7 1/2`, x ∈ 1

Answer 1

`-81/2 < -1/2-4x<=71/2`, x ∈ I

`=> -17/2 < -1/2 - 4x <= 15/2`, x ∈ I

Take  `-17/2 < -1/2 - 4x`      `-1/2 - 4x <= 15/2`

`-17/2 + 1/2 < -4x`              `-4x <= 15/2 + 1/2`

`-16/2 < -4x`                        `-4x <= 16/2`

-8 < -4x                                  `-4x <= 8`       

2 > x                                      `x >= -2`

Thus, on simplifying, the given inequation reduces to -2 ≤ x 2.

Since x ∈ I, the solution set is { -2, -1, 0, 1}.

The required graph on the number line is as follows: