Question

How do you solve `|2x + 9| < 25`?

Answer 1

The solution is x is in the range: `-17 < x < 8`

Explanation:

Because this problem involves and inequality with an absolute value function we must set up a system of inequalities because the absolute value function will transform a negative or positive number to a positive number. We can rewrite this problem as:

`-25 < 2x + 9 < 25`

Now we can solve for `x` while keeping the entire system balanced:

`-25 - 9 < 2x + 9 - 9 < 25 - 9`

`-34 < 2x < 16`

`(-34)/2 < (2x)/2 < 16/2`

`-17 < (cancel(2)x)/cancel(2) < 8`

`-17 < x < 8`