SOLUTION: Did I get the right answer? -1/3-2x/3>1/3 and -7x-1/2<6 1/2 my answer: x>1 and x<-1

Algebra ->  Inequalities -> SOLUTION: Did I get the right answer? -1/3-2x/3>1/3 and -7x-1/2<6 1/2 my answer: x>1 and x<-1      Log On


   

Question 163038This question is from textbook saxon algebra 2
: Did I get the right answer?
-1/3-2x/3>1/3 and -7x-1/2<6 1/2
my answer: x>1 and x<-1 This question is from textbook saxon algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to find the solution set of the system of inequalites -1%2F3-2x%2F3%3E1%2F3 AND -7x-1%2F2%3C6%261%2F2+ right?


-1%2F3-2x%2F3%3E1%2F3 Start with the first inequality.


3%28-1%2Fcross%283%29-2x%2Fcross%283%29%29%3E3%281%2Fcross%283%29%29 Multiply both sides by the LCD 3 to clear any fractions.


-1-2x%3E1 Distribute and multiply.


-2x%3E1%2B1 Add 1 to both sides.


-2x%3E2 Combine like terms on the right side.


x%3C%282%29%2F%28-2%29 Divide both sides by -2 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3C-1 Reduce.


So the first part of the answer is x%3C-1


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-7x-1%2F2%3C6%261%2F2 Start with the second inequality


-7x-1%2F2%3C13%2F2 Convert the mixed fraction into an improper fraction.


2%28-7x-1%2Fcross%282%29%29%3C2%2813%2Fcross%282%29%29 Multiply both sides by the LCD 2 to clear any fractions.


-14x-1%3C13 Distribute and multiply.


-14x%3C13%2B1 Add 1 to both sides.


-14x%3C14 Combine like terms on the right side.


x%3E%2814%29%2F%28-14%29 Divide both sides by -14 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E-1 Reduce.


So the second part of the answer is x%3E-1


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Answer:

So together the answers are x%3C-1 AND x%3E-1

This is NOT possible since you cannot have a number that is both less and greater than some number. It's like saying "pick a number that is BOTH positive AND negative", it's not possible.


So there are no solutions