SOLUTION: 1/4{5x-1/2}-1/3<2/3 use builder notation and solve {xlx } the l is post to be a straight line

Algebra ->  Algebra  -> Inequalities -> SOLUTION: 1/4{5x-1/2}-1/3<2/3 use builder notation and solve {xlx } the l is post to be a straight line      Log On

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Question 151534: 1/4{5x-1/2}-1/3<2/3 use builder notation and solve {xlx } the l is post to be a straight line
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F4%29%285x-1%2F2%29-1%2F3%3C2%2F3 Start with the given inequality.


%285%2F4%29x-1%2F8-1%2F3%3C2%2F3 Distribute.


24%28%285%2Fcross%284%29%29x-1%2Fcross%288%29-1%2Fcross%283%29%29%3C24%282%2Fcross%283%29%29 Multiply both sides by the LCD 24 to clear any fractions.


30x-3-8%3C16 Distribute and multiply.


30x-11%3C16 Combine like terms on the left side.


30x%3C16%2B11 Add 11 to both sides.


30x%3C27 Combine like terms on the right side.


x%3C%2827%29%2F%2830%29 Divide both sides by 30 to isolate x.


x%3C9%2F10 Reduce.


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Answer:

So the answer is x%3C9%2F10


Which approximates to x%3C0.9



So the solution set is


Also, the answer in interval notation is



Here's the graph of the solution set

drawing%28500%2C80%2C-5%2C+10%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-5%2C+10%29%2C%0D%0A%0D%0A%0D%0Aarrow%289%2F10%2C0%2C-5%2C0%29%2C%0D%0Aarrow%289%2F10%2C0.30%2C-5%2C0.30%29%2C%0D%0Aarrow%289%2F10%2C0.15%2C-5%2C0.15%29%2C%0D%0Aarrow%289%2F10%2C-0.15%2C-5%2C-0.15%29%2C%0D%0Aarrow%289%2F10%2C-0.30%2C-5%2C-0.30%29%2C%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Acircle%289%2F10%2C0%2C0.2%29%2C%0D%0Acircle%289%2F10%2C0%2C0.2%29%2C%0D%0Acircle%289%2F10%2C0%2C0.2%29%2C%0D%0Acircle%289%2F10%2C0%2C0.2-0.02%29%0D%0A%29

Note: there is an open circle at x=0.9