Question 1099191: What Is the value of n that satisfies the equation below
-5(2n+3)+3(3n+4)= -8
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! What Is the value of n that satisfies the equation below
-5(2n+3)+3(3n+4)= -8
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The process is called "solving for n" (you will see "solving for x" a lot in Algebra, the letter is merely a placeholder). What we want is n by itself ("one n") on one side of the equation and some number on the other side.
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First, distribute (multiply within parenthesis) the -5 and we will also distribute the 3 into its parenthesis as well:
(-10n - 15) + (9n + 12) = -8
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Re-writing without parenthesis:
-10n -15 + 9n +12 = -8
[ side note: when removing parenthesis, if you have something like " - (a + b - c)" the signs will all change when you remove the parenthesis, so you'd write: " -a - b + c ". ]
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Now collect like-terms (this just means adding the coefficients of "n" terms, and adding the constants… but in the future you will see things like  or  — just remember collecting like-terms applies similarly):
-n - 3 = -8
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Now, since we have all negative terms, we can multiply both sides by -1:
(-1)(-n - 3) = (-1)(-8)
n + 3 = 8 (as long as you do the same operation to both sides, the equality is retained)
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Finally, just subtract 3 from each side:
n + 3 - 3 = 8 - 3
n + 0 = 5
ANS: n = 5
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Check:
To do the check, we plug in n=5 in the original equation and check that both sides are equal. Here we can work just with the left side and note that the computation should give us -8:
-5 (2(5)+3)+3(3(5) + 4) = -5(13) + (3(19)) = -65 + 57 = -8 (ok)
Answer by ikleyn(52781)  (Show Source):
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