SOLUTION: what does |x-1/3| less than 16/3 equal? i tried splitting the problem into two: [(x-1/3) less than 16/3] and [(x-1/3) greater than -16/3] this was not correct. what was wrong?

Algebra ->  Absolute-value -> SOLUTION: what does |x-1/3| less than 16/3 equal? i tried splitting the problem into two: [(x-1/3) less than 16/3] and [(x-1/3) greater than -16/3] this was not correct. what was wrong?      Log On


   



Question 919603: what does |x-1/3| less than 16/3 equal?
i tried splitting the problem into two:
[(x-1/3) less than 16/3] and [(x-1/3) greater than -16/3]
this was not correct. what was wrong?

Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
What? That is an inequality. An inequality is an inequality. The left side unequal to the right side according to the ordering used.

You indicate abs%28x-1%2F3%29%3C16%2F3. The inequality just is.

Your next statement could use some analysis and maybe solving of the inequality.

If the argument inside absolute value function is zero or positive, then:
x-1%2F3%3C16%2F3
x%3C16%2F3%2B1%2F3
x%3C17%2F3
If the argument is negative, then:
-%28x-1%2F3%29%3C16%2F3
-x%2B1%2F3%3C16%2F3
-x%3C16%2F3-1%2F3
-x%3C15%2F3
-x%3C5
Multiply both sides by NEGATIVE 1, which reverses the order symbol,
x%3E-5
-
The solution is, EITHER x%3C17%2F3 OR x%3E-5;
when you put both of these solution parts together, they share a set of values:
highlight%28-5%3Cx%3C17%2F3%29.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-1%29%2F3+%3C16%2F3...I assume you have this
%28x-1%29%2F3+%3C16%2F3 .......cross multiply
%28x-1%293+%3C16%2A3
%28x-1%29cross%283+%29%3C16%2Across%283%29
x-1+%3C16
x+%3C16%2B1
x+%3C17
but, if you have x-1%2F3+%3C16%2F3, then
3x%2F3-1%2F3+%3C16%2F3
%283x-1%29%2Fcross%283%29+%3C16%2Fcross%283%29
3x-1+%3C16
3x+%3C16%2B1
3x+%3C17
x+%3C17%2F3

you tried splitting the problem into two:
[(x-1/3) less than 16/3] and [(x-1/3) greater than -16/3]
you cannot do that when you are given only "less+than"