# How do you solve and write the following in interval notation: #|8-3x|>5#?

##### 2 Answers

See the entire solution process below:

#### Explanation:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

First, subtract

Now, divide each segment by

Or

Or, in interval form:

#### Explanation:

Inequalities of the form

#|x|>a# have solutions in the form.

#x<-acolor(red)" or " x>a#

#rArr8-3x< -5color(red)" OR " 8-3x>5#

#rArr-3x<-13color(red)" OR " -3x> -3#

#color(white)(XXX)rArrx> 13/3 color(red)" OR " x <1# [Remember to

#color(blue)"reverse signs"# when multiplying or dividing by a#color(blue)"negative quantity"]#

#"Expressed in interval notation as"#

#(-oo,1)uu(13/3,+oo)#