SOLUTION: set notation and graph it:-2(3+x)<4x+4<8x

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Question 207433: set notation and graph it:-2(3+x)<4x+4<8x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-2%283%2Bx%29%3C4x%2B4%3C8x Start with the given compound inequality.


-6-2x%3C4x%2B4%3C8x Distribute



Break up the compound inequality to get:


-6-2x%3C4x%2B4 AND 4x%2B4%3C8x


So let's solve the first inequality -6-2x%3C4x%2B4


-6-2x%3C4x%2B4 Start with the given inequality.


-2x%3C4x%2B4%2B6 Add 6 to both sides.


-2x-4x%3C4%2B6 Subtract 4x from both sides.


-6x%3C4%2B6 Combine like terms on the left side.


-6x%3C10 Combine like terms on the right side.


x%3E%2810%29%2F%28-6%29 Divide both sides by -6 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E-5%2F3 Reduce.


Now let's solve the second inequality 4x%2B4%3C8x


4x%2B4%3C8x Start with the given inequality.


4x%3C8x-4 Subtract 4 from both sides.


4x-8x%3C-4 Subtract 8x from both sides.


-4x%3C-4 Combine like terms on the left side.


x%3E%28-4%29%2F%28-4%29 Divide both sides by -4 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E1 Reduce.



If we combine the results x%3E-5%2F3 and x%3E1 we get x%3E1


Note: we're essentially performing a set intersection between the two results.

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Answer:

So the solution is x%3E1


So the answer in set-builder notation is



Here's the graph of the solution set