To solve the equation 2|3x + 4y - 2| + 3/25 - 5x + 2 = 0, we can break it down into two cases based on the absolute value:
Case 1: 3x + 4y - 2 is non-negative (i.e., 3x + 4y - 2 ≥ 0):
In this case, we have:
2(3x + 4y - 2) + 3/25 - 5x + 2 = 0
Now, let's simplify this equation:
6x + 8y - 4 + 3/25 - 5x + 2 = 0
Combine like terms:
(6x - 5x) + 8y - 4 + 3/25 + 2 = 0
x + 8y - 4 + 3/25 + 2 = 0
Now, isolate x:
x = 4 - 3/25 - 2 - 8y
x = (4 - 2) - (3/25) - 8y
x = 2 - 3/25 - 8y
Case 2: 3x + 4y - 2 is negative (i.e., 3x + 4y - 2 < 0):
In this case, we have:
2(-(3x + 4y - 2)) + 3/25 - 5x + 2 = 0
Now, let's simplify this equation:
-2(3x + 4y - 2) + 3/25 - 5x + 2 = 0
Distribute the -2:
-6x - 8y + 4 + 3/25 - 5x + 2 = 0
Combine like terms:
(-6x - 5x) - 8y + 4 + 3/25 + 2 = 0
-11x - 8y + 4 + 3/25 + 2 = 0
Now, isolate x:
-11x = -4 - 3/25 - 2 + 8y
x = (4 + 2) + (3/25) + 8y
x = 6 + 3/25 + 8y
So, we have two possible solutions:
1. If 3x + 4y - 2 is non-negative, then x = 2 - 3/25 - 8y.
2. If 3x + 4y - 2 is negative, then x = 6 + 3/25 + 8y.
These are the solutions to the given equation, depending on the value of 3x + 4y - 2.