SOLUTION: how would you solve this problem 1 = -3 + |2 - 1/4y|

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Question 620925: how would you solve this problem
1 = -3 + |2 - 1/4y|
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
First, I would add 3 to both sides of the equal sign to get a more convenient, equivalent equation:
1=-3%2Babs%282-%281%2F4%29y%29 --> 1%2B3=-3%2B3%2Babs%282-%281%2F4%29y%29 --> 4=abs%282-%281%2F4%29y%29
Then I would split the problem into two cases (two equations) and I would solve each equation, getting a total of two solutions.
If 2-%281%2F4%29y%3E=0, the equation is 2-%281%2F4%29y=4
If 2-%281%2F4%29y%3C0, the equation is -%282-%281%2F4%29y%29=4 or (multiplying both sides of the equal sign times (-1) ),
2-%281%2F4%29y=-4
To solve 2-%281%2F4%29y=4, I would first subtract 2 from both sides.
Then I would multiply both sides times (-4).
2-%281%2F4%29y=4 -->2-2-%281%2F4%29y=4-2 --> -%281%2F4%29y=2 --> -4%2A%28-1%2F4%29y%29=%28-4%29%2A2 --> y=-8
I would solve 2-%281%2F4%29y=4 the same way
2-%281%2F4%29y=-4 -->2-2-%281%2F4%29y=-4-2 --> -%281%2F4%29y=-6 --> -4%2A%28-1%2F4%29y%29=%28-4%29%2A%28-6%29 --> y=24