Question

Solve the compound inequality 2x > –10 and 3x < 24.

A) –5 < x < 8

B) 5 > x > –8

C) 5 > x < –8

D) –5 < x > 8

Answer 1

For this case we have the following inequalities:

`2x> -10` intersected with
`3x <24`

So:

`2x> -10`

Dividing between 2 on both sides:

`x> - \frac {10} {2}\\x> -5`

The solution is given by all values of strict x greater than -5.

On the other hand we have:

`3x <24`

Dividing between 3 on both sides:

`x <\frac {24} {3}\\x <8`

The solution is given by all values of x less strict to 8.

Intersecting the solutions we have:

`(-5,8)`

Answer:

`-5 <x <8`