SOLUTION: the absolute value of 1/2x - 1 < 1

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Question 119825: the absolute value of 1/2x - 1 < 1
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

abs%28%281%2F2%29x-1%29%3C1 Start with the given inequality


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

%281%2F2%29x-1+%3E+-1 and %281%2F2%29x-1+%3C+1 Break up the absolute value inequality using the given rule


-1+%3C+%281%2F2%29x-1+%3C+1 Combine the two inequalities to get a compound inequality



0+%3C+%281%2F2%29x+%3C+2 Add 1 to all sides



0+%3C+x+%3C+4 Multiply all sides by 2 to isolate x


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Answer:

So our answer is

0+%3C+x+%3C+4



which looks like this in interval notation






if you wanted to graph the solution set, you would get

drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-8%2C+12%29%2C%0D%0A%0D%0Ablue%28line%28-1.5%2C-7%2C1.65%2C-7%29%29%2C%0D%0Ablue%28line%28-1.5%2C-6%2C1.65%2C-6%29%29%2C%0D%0Ablue%28line%28-1.5%2C-5%2C1.65%2C-5%29%29%2C%0D%0A%0D%0Acircle%28-2%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-2%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-2%2C-5.8%2C0.45%29%2C%0D%0A%0D%0A%0D%0Acircle%282%2C-5.8%2C0.35%29%2C%0D%0Acircle%282%2C-5.8%2C0.4%29%2C%0D%0Acircle%282%2C-5.8%2C0.45%29%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%29 Graph of the solution set in blue and the excluded values represented by open circles