How do you solve #abs(2/3x-1/3)<=1/3#?

1 Answer
MathFact-orials.blogspot.com
Feb 26, 2017

#0<= x <= 1#

Explanation:

When working with absolute value questions, we need to remember that #abs(x)=pmx#. We need to evaluate both the positive and negative values of the absolute value term.

Positive

#abs(2/3x-1/3)<=1/3#

#2/3x-1/3<=1/3#

#2/3x<=2/3#

#x<=1#

Negative

#abs(2/3x-1/3)<=1/3#

#-(2/3x-1/3)<=1/3#

#-2/3x+1/3<=1/3#

#-2/3x<=0#

#x>=0#

Putting them together:

#0<= x <= 1#

Related questions
See all questions in Absolute Value Inequalities
Impact of this question
1420 views around the world
You can reuse this answer
Creative Commons License