SOLUTION: 5x+5<3(x+2)

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Question 150976: 5x+5<3(x+2)
Answer by jim_thompson5910(14872) About Me  (Show Source):
You can put this solution on YOUR website!

5x%2B5%3C3%28x%2B2%29 Start with the given inequality.


5x%2B5%3C3x%2B6 Distribute.


5x%3C3x%2B6-5 Subtract 5 from both sides.


5x-3x%3C6-5 Subtract 3x from both sides.


2x%3C6-5 Combine like terms on the left side.


2x%3C1 Combine like terms on the right side.


x%3C%281%29%2F%282%29 Divide both sides by 2 to isolate x.


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Answer:

So the answer is x%3C1%2F2


Which approximates to x%3C0.5




So the answer in interval notation is




Also, the answer in set-builder notation is



Here's the graph of the solution set

drawing%28500%2C80%2C-9%2C+11%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-9%2C+11%29%2C%0D%0A%0D%0A%0D%0Aarrow%281%2F2%2C0%2C-9%2C0%29%2C%0D%0Aarrow%281%2F2%2C0.30%2C-9%2C0.30%29%2C%0D%0Aarrow%281%2F2%2C0.15%2C-9%2C0.15%29%2C%0D%0Aarrow%281%2F2%2C-0.15%2C-9%2C-0.15%29%2C%0D%0Aarrow%281%2F2%2C-0.30%2C-9%2C-0.30%29%2C%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Acircle%281%2F2%2C0%2C0.3%29%2C%0D%0Acircle%281%2F2%2C0%2C0.3%29%2C%0D%0Acircle%281%2F2%2C0%2C0.3%29%2C%0D%0Acircle%281%2F2%2C0%2C0.3-0.02%29%0D%0A%29