SOLUTION: Find the solutions of the inequality {{{15<3x-3(x-5)/2<=30}}}

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Question 150306: Find the solutions of the inequality
15%3C3x-3%28x-5%29%2F2%3C=30
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
Find the solutions of the inequality
15%3C3x-3%28x-5%29%2F2%3C=30 

In a three sides inequality we solve for x in 
the middle:

Clear of fractions by multiplying all three
sides by 2:

2%2815%29%3C2%283x-3%28x-5%29%2F2%29++%3C=2%2830%29

30%3C2%2A3x-2%2A3%28x-5%29%2F2%3C=60

30%3C2%2A3x-cross%282%29%2A3%28x-5%29%2Fcross%282%29%3C=60

30%3C6x-3%28x-5%29%3C=60

30%3C6x-3x%2B15%3C=60

30%3C3x%2B15%3C=60

Subtract 15 for all three sides:

30-15%3C3x%2B15-15%3C=60-15

15%3C3x%3C=45

Divide all three sides by 3:

15%2F3%3C3x%2F3%3C=45%2F3

5%3Cx%3C=15

If you have had interval notation,

the interval notation is (5,15]

Edwin