SOLUTION: -3(x+1)+4(-x-2)-3(-x+4) if x=-1/2 I'm having a problem with all the (-) and the fraction

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Question 67545This question is from textbook intermediate algebra
: -3(x+1)+4(-x-2)-3(-x+4) if x=-1/2
I'm having a problem with all the (-) and the fraction This question is from textbook intermediate algebra

Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
Having problems with minus signs and fractions is common, so pay attention:
-3%281%2F2%2B1%29%2B4%28-1%2F2-2%29-3%28-1%2F2%2B4%29
To sum and subtract fractions, we need the lcm (least common multiple) of the two fractions. If you relate the natural numbers to fractions with denominator 1, it's easy to see that the lcm is 2, for all the parentheses. Don't forget to multiply the denominator by 2 accordingly:
-3%281%2F2%2B2%2F2%29%2B4%28-1%2F2-4%2F2%29-3%28-1%2F2%2B8%2F2%29
Now we just sum the numerators (don't forget the minus signs!):
-3%283%2F2%29%2B4%28-5%2F2%29-3%287%2F2%29
To multiply fractions by natural numbers, we just multiply the numerator by the
number and conserve the denominator. Pay attention to the minus signs, yet again! (two equal signs = plus, two different signs = minus is a good rule to remember)

-9%2F2-20%2F2-21%2F2
Just sum, the denominators are equal!
-50%2F2
Division works the same as multiplication: two different signs, so we get a negative as result:
-25