SOLUTION: Find the solution set {{{-3/2<(3(2x-4))/5<=2}}}

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Question 124677: Find the solution set

-3%2F2%3C%283%282x-4%29%29%2F5%3C=2

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
-3%2F2%3C%283%282x-4%29%29%2F5%3C=2 Start with the given compound inequality


10%28-3%2F2%29%3C10%28%283%282x-4%29%29%2F5%29%3C=10%282%29 Multiply all sides by the LCD 10. This will eliminate the fractions


-15%3C6%282x-4%29%3C=20 Distribute and multiply


-15%3C12x-24%3C=20 Distribute again




9%3C12x%3C=44 Add 24 to all sides






9%2F12%3Cx%3C=44%2F12 Divide every side by 12 to isolate x.


3%2F4%3Cx%3C=11%2F3 Reduce.



So the solution in interval notation is: (3%2F4,11%2F3]


Now let's graph the solution set

drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-7.79166666666667%2C+12.2083333333333%29%2C%0D%0Ablue%28line%28-1.20833333333333%2C-7%2C1.30833333333333%2C-7%29%29%2C%0D%0Ablue%28line%28-1.20833333333333%2C-6%2C1.30833333333333%2C-6%29%29%2C%0D%0Ablue%28line%28-1.20833333333333%2C-5%2C1.30833333333333%2C-5%29%29%2C%0D%0A%0D%0Acircle%28-1.45833333333333%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-1.45833333333333%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-1.45833333333333%2C-5.8%2C0.45%29%2C%0D%0A%0D%0Acircle%281.45833333333333%2C-5.8%2C0.10%29%2C%0D%0Acircle%281.45833333333333%2C-5.8%2C0.15%29%2C%0D%0Acircle%281.45833333333333%2C-5.8%2C0.20%29%2C%0D%0Acircle%281.45833333333333%2C-5.8%2C0.25%29%2C%0D%0Acircle%281.45833333333333%2C-5.8%2C0.30%29%2C%0D%0Acircle%281.45833333333333%2C-5.8%2C0.35%29%2C%0D%0Acircle%281.45833333333333%2C-5.8%2C0.40%29%0D%0A%0D%0A%0D%0A%29

Note: at x=3%2F4 there is a open circle (which means this point is excluded) and at x=11%2F3 there is a closed circle (which means this point is included)