Which of the following is the solution to the compound inequality below? 3x+5>-1 or -2x-7>5

Question

asked Apr 10, 2020 88.0k views

1 Answer

Brandon Wood · Answer 1 · 2020-04-17T09:02:06+0000

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, ∞)