SOLUTION: Solve (2x-3)/6<=-9 or (2x-3)/6>=1

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Question 193076: Solve (2x-3)/6<=-9 or (2x-3)/6>=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve the first inequality %282x-3%29%2F6%3C=-9:


%282x-3%29%2F6%3C=-9 Start with the first inequality.


2x-3%3C=6%28-9%29 Multiply both sides by 6.


2x-3%3C=-54 Multiply.


2x%3C=-54%2B3 Add 3 to both sides.


2x%3C=-51 Combine like terms on the right side.


x%3C=%28-51%29%2F%282%29 Divide both sides by 2 to isolate x.


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Now let's solve the second inequality %282x-3%29%2F6%3E=1:


%282x-3%29%2F6%3E=1 Start with the second inequality.


2x-3%3E=6%281%29 Multiply both sides by 6.


2x-3%3E=6 Multiply.


2x%3E=6%2B3 Add 3 to both sides.


2x%3E=9 Combine like terms on the right side.


x%3E=%289%29%2F%282%29 Divide both sides by 2 to isolate x.


So our answer is x%3C=-51%2F2 or x%3E=9%2F2


Which in set-builder notation looks like