SOLUTION: What is the sum of all the solutions of x = |2x-|60-2x||?

Question 1148536: What is the sum of all the solutions of x = |2x-|60-2x||?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Find equivalent expressions for the given function

for different ranges of values for x.

Case 1: x>30

When x>30, 2x>60, and (60-2x) is negative; that means

and then

So on the interval x>30, the only solution to the given equation is x=60.

Case 2: x<30

When x<30, 2x<60, and (60-2x) is positive; that means

and then

is positive for x<15 and negative for x>15, so we need to break case 2 into two sub-cases.

Case 2a: x<15

So on the interval x<15, the solution to the given equation will be when

Case 2b: x>15 and x<30

So on the interval (15,30), the solution to the given equation will be when

ANSWER: There are three solutions to the equation: x=12, x=20, and x=60.

A graph....

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