posted by Anonymous .
I am re posting this for fear that it was overlooked earlier. I have also decided to show my work in the hopes of preventing any issues that might arise.
Solve the absolute value equation.
I y+3 I +5=2y
Would the solutions be 8=y and y=2/3?
Subtract 5 from both sides.
I y+3 I = 2y-5
y+3=2y-5 And y+3= -(2y-5)
subtract "y" from the first equation.
Add 2y to the equation y+3= -(2y-5) which had become y+3= -2y+5
Now, the two equations are 3=y-5 and 3y+3=5.
Add 5 to both sides of the first equation. Get 8=y.
Subtract 3 from each side of the second equation. Get 3y=2. Divide by 3. Get y=2/3.
Hence, y=8, y=2/3.
I'm totally with you on y=8, but the best way to check your answer is to substitute the value back in.
Now try y=2/3:
Is |2/3+3| + 5 = 2(2/3) ?
Is 11/3 + 15/3 = 4/3 ?
I think you took a wrong turn at: "Now, the two equations are 3=y-5 and 3y+3=5."
You can't assume you can break up the absolute that way.
Is 8 the only answer?
Well, y can't be less than 2.5, because |y+3|>=0 and 5 is 5, so |y+3|+5 >=5, so 2y cannot be less than 5.
Since y can't be negative, |y+3| must equal y+3, so the equation is simply equivalent to y+3+5=2y, so 8 is the only answer.