Question

Which of the following is the solution to the compound inequality below?

3x+5>-1 or -2x-7>5

Answer 1

For this case we have:

`3x + 5> -1`

Subtracting 5 from both sides of the inequality:

`3x> -1-5\\3x> -6`

Dividing between 3 on both sides:

`x> - \frac {6} {3}\\x> -2`

The solution is given by all values of strict x greater than -2.

On the other hand we have:

`-2x-7> 5`

Adding 7 to both sides:

`-2x> 5 + 7\\-2x> 12`

Dividing between 2 on both sides:

`-x> \frac {12} {2}\\-x> 6`

We multiply by -1 on both sides taking into account that the sense of inequality changes:

`x <6`

The solution is given by all values of x less strict to 6.

Finally the solution is:

(-∞, 6) U (-2, ∞)

ANswer:

(-∞, 6) U (-2, ∞)