Question

How do you solve `5| x + 1| > 10`?

Answer 1

`x> -3 or x>1`

Explanation:

First, simplify the inequality as much as possible before you deal with the absolute value term:

`5|x+1| > 10`
`color(white)"x" |x+1| > 2 color(white)"XXX"` (dividing both sides by 5)

Therefore, `x+1` must either be greater than 2, or less than -2 for the equation to be true. So, we can split this equation into two equations and solve both of them to get our solution.

`color(white)"XXXXXXX" |x+1| > 2`

`x+1 > 2 color(white)"XXX" or color(white)"XXX" x+1 < -2`
`color(white)"X-X" x > 1 color(white)"XXX" or color(white)"XXXX-X" x < -3`

So our final solution is:

`x> -3 or x>1`

Or if the problem asks for interval notation:

`(-oo, -3) uu (1, oo)`

Final Answer