The answer: {-14/5,2}{−145,2}
Absolute value operation always return non-negative.
So,
if (5y+2)/2>=0 ->abs((5y+2)/2) = (5y+2)/2
if (5y+2)/2<0 ->abs((5y+2)/2) = (-1) * ((5y+2)/2)
Since we don't know the value of y, we need to check all these possibilities.
First
Assume that (5y+2)/2 >= 0
We need to find the range of y
2 * ((5y+2)/2) >= 2 * 0
5y +2 >= 0
A: y>=-2/5
We need to remember this.
Now, try to solve the given equation.
(5y+2)/2 = 6
5y+2=12
5y=10
y = 2
Remember expression A, y=2 satisfies the inequality in expression A. So 2 is in the solution set.
Second
Assume that (5y+2)/2<0
B: y < -2/5
Now try to solve the given equation again, but this time the absolute value operation will return (-1) times of the input since the input is assumed negative.
(-1) * (5y+2)/2 = 6
(5y+2)/2 = -6
5y+2 = -12
5y = -14
y = -14/5
y=-14/5 satisfies the inequality in the expression B so -14/5 is also in our solution set.
Result: {-14/5,2}