SOLUTION: I need quick help on solving this , hope you can help , thanks . x-1 over 5(as a fraction) minus x+2 over 6(as a fraction) ≥ 7/15 need to show work

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Question 611104: I need quick help on solving this , hope you can help , thanks . x-1 over 5(as a fraction) minus x+2 over 6(as a fraction) ≥ 7/15 need to show work
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-1%29%2F5+-+%28x%2B2%29%2F6+%3E=+7%2F15
First, I like to change the subtraction to an addition. I've found that trying to leave subtractions as subtractions, especially when fractions are involved, makes it much more likely to make a mistake.
%28x-1%29%2F5+%2B+%28-%28x%2B2%29%29%2F6+%3E=+7%2F15
or
%28x-1%29%2F5+%2B+%28-x-2%29%2F6+%3E=+7%2F15

The simplest way to solve inequalities (or equations) with fractions like this is, IMHO, to start by eliminating the fractions. The fractions can be eliminated by multiplying both sides of the inequality (or equation) by the lowest common denominator (LCD) of all the fractions. The LCD of 5, 6 and 15 is 30. So we will multiply each side by 30:
30%28%28x-1%29%2F5+%2B+%28-x-2%29%2F6%29+%3E=+30%287%2F15%29
(Note: Since we multiplied both sides by a positive number, we did not have to reverse the inequality like we would have if we multiplied by a negative number.) On the left side we need to use the Distributive Property:
30%28%28x-1%29%2F5%29+%2B+30%28%28-x-2%29%2F6%29+%3E=+30%287%2F15%29
Now when we multiply, all the denominators cancel out!
6%28x-1%29+%2B+5%28-x-2%29+%3E=+2%287%29
which simplifies as follows:
6x-6%2B%28-5x%29%2B%28-10%29+%3E=+14
x+%2B+%28-16%29+%3E=+14
Now we solve for x. Adding 16 to each side we get:
x+%3E=+30