SOLUTION: 3 /2x-4/ -5<7

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Question 119121: 3 /2x-4/ -5<7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Aabs%282x-4%29-5%3C7 Start with the given inequality


3%2Aabs%282x-4%29%3C12 Add 5 to both sides.


abs%282x-4%29%3C4 Divide both sides by 3




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

2x-4+%3E+-4 and 2x-4+%3C+4 Break up the absolute value inequality using the given rule


-4+%3C+2x-4+%3C+4 Combine the two inequalities to get a compound inequality



0+%3C+2x+%3C+8 Add 4 to all sides


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

Graph of the solution set in blue and the excluded values represented by open circles