Expert: Sherman D. - 6/17/2009

Question
QUESTION: solve |1-2x|<1/3

i tried working it, but it is just confusing. please help !!

ANSWER: |1 - 2x| < (1/3)

this can be thought of as

-(1 - 2x) < (1/3) or 1 - 2x < (1/3)

1 - 2x > (-1/3) or 1 - 2x < (1/3)

-2x > (-1/3) - 1 or -2x < (1/3) - 1

-2x > (-1/3) - (3/3) or -2x < (1/3) - (3/3)

-2x > (-4/3) or -2x < (-2/3)

x > (4/6) or x < (2/6)

x > (2/3) or x < (1/3)

your answer is written like this (1/3) > x > (2/3)

www.quickmath.com will give you the answer for you.

---------- FOLLOW-UP ----------

QUESTION: sorry to bother you, I have a small doubt, when you have absolute value symbol the 1-2x changes to 1+2x right ?

Thank you !

Answer
here is proof of my answer, go to www.quickmath.com

click on Solve which is located under Inequalities, then type in

|1 - 2x| < (1/3)

now click Solve and what does it get, but the exact same value as my answer.

when you change one you have to change everything in the absolute value, but it would be easier to just divide both sides by + and - instead.

however if (1/3) had been (-1/3) to begin with, then you wouldn't be able to find a solution.