Question 1208820: Find all c such that |c + 5| - 3c = 10 - 5|c - 1| + 7|c + 8|.
Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The "behavior" of the expression changes at each value of c for which one of absolute value expressions is equal to 0. Those values are -8, -5, and 1.
Use those three values of c to divide the number line into four intervals and look for values in each interval that satisfy the given equation.
To make the analysis a bit easier, I will change the form of the equation so I can look for a zero value for the entire expression:

(1) On the interval (-infinity,-8)....



The expression is





This "solution" is not in the interval for this case, so it is not a solution.
(2) On the interval [-8,-5)....



The expression is





This "solution" is also not in the interval for this case, so it also is not a solution.
(3) On the interval [-5,1)....



The expression is





This "solution" IS in the interval for this case, so it IS a solution.
(4) On the interval [1,infinity)....



The expression is





This "solution" is once again not in the interval for this case, so it is not a solution.
ANSWER: There is a single solution: c = -4
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