# How do you solve and write the following in interval notation: 4abs[x+1]-2<10?

Apr 24, 2018

Solution: $- 4 < x < 2$ , Interval notation : $x | \left(- 4 , 2\right)$

#### Explanation:

$4 | x + 1 | - 2 < 10 \mathmr{and} 4 | x + 1 | < 12$ or

$| x + 1 | < 3 \therefore \left(x + 1\right) < 3 \mathmr{and} x < 2$ OR

$\left(x + 1\right) > - 3 \mathmr{and} x > - 4$

Solution: $- 4 < x < 2$ , Interval notation : $x | \left(- 4 , 2\right)$ [Ans]