How do you solve and write the following in interval notation: #| 2x – 4 | ≤ 12#?

1 Answer
smendyka
Apr 28, 2017

See the entire solution process below:

Explanation:

The absolute value function takes any term, negative or positive, and transforms it to its positive form. Therefore, you need to solve the term inside the absolute value for both the positive and negative version of what it is equated to.

#-12 <= 2x - 4 <= 12#

#-12 + color(red)(4) <= 2x - 4 + color(red)(4) <= 12 + color(red)(4)#

#-8 <= 2x - 0 <= 16#

#-8 <= 2x <= 16#

#-8/color(red)(2) <= (2x)/color(red)(2) <= 16/color(red)(2)#

#-4 <= (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) <= 8#

#-4 <= x <= 8#

Or

#x >= -4# and #x <= 8#

Or, in interval notation

#[-4, 8]#

Related questions
See all questions in Absolute Value Inequalities
Impact of this question
1398 views around the world
You can reuse this answer
Creative Commons License