SOLUTION: 5/4[x-1/2]-5/3<4/3 Please help I need to use set builder to fill this in {x/x? ?}

Algebra ->  Absolute-value -> SOLUTION: 5/4[x-1/2]-5/3<4/3 Please help I need to use set builder to fill this in {x/x? ?}      Log On


   

Question 200028: 5/4[x-1/2]-5/3<4/3
Please help I need to use set builder to fill this in
{x/x? ?}
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2F4%29%2Aabs%28x-1%2F2%29-5%2F3%3C4%2F3 Start with the given inequality.


%285%2F4%29%2Aabs%28x-1%2F2%29%3C4%2F3%2B5%2F3 Add 5%2F3 to both sides.


%285%2F4%29%2Aabs%28x-1%2F2%29%3C9%2F3 Combine like terms.


%285%2F4%29%2Aabs%28x-1%2F2%29%3C3 Reduce


5%2Aabs%28x-1%2F2%29%3C3%2A4 Multiply both sides by 4.


5%2Aabs%28x-1%2F2%29%3C12 Multiply


abs%28x-1%2F2%29%3C12%2F5 Divide both sides by 5.


Break up the absolute value (remember, if you have abs%28x%29%3C+a, then x+%3E+-a and x+%3C+a)


x-1%2F2+%3E+-12%2F5 and x-1%2F2+%3C+12%2F5 Break up the absolute value inequality using the given rule


-12%2F5+%3C+x-1%2F2+%3C+12%2F5 Combine the two inequalities to get a compound inequality


Multiply EVERY term on ALL sides by the LCD 10 to clear out the fractions.


-24%3C10x-5%3C24 Multiply and simplify


-24%2B5%3C10x%3C24%2B5 Add 5 to ALL sides.


-19%3C10x%3C24%2B5 Combine like terms on the left side.


-19%3C10x%3C29 Combine like terms on the right side.


%28-19%29%2F10%3Cx%3C%2829%29%2F10 Divide all sides by 10.



So the solution is -19%2F10%3Cx%3C29%2F10

So the answer in set-builder notation is