SOLUTION: the inequality 1/2x+3<2x-6 is equivalent to

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Question 171396This question is from textbook
: the inequality 1/2x+3<2x-6 is equivalent to This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2F2%29x%2B3%3C2x-6 Start with the given inequality.


2%28%281%2Fcross%282%29%29x%2B3%29%3C2%282x-6%29 Multiply both sides by the LCD 2 to clear any fractions.


x%2B6%3C4x-12 Distribute and multiply.


x%3C4x-12-6 Subtract 6 from both sides.


x-4x%3C-12-6 Subtract 4x from both sides.


-3x%3C-12-6 Combine like terms on the left side.


-3x%3C-18 Combine like terms on the right side.


x%3E%28-18%29%2F%28-3%29 Divide both sides by -3 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E6 Reduce.


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Answer:

So the answer is x%3E6


So this means that %281%2F2%29x%2B3%3C2x-6 is equivalent to x%3E6