Solve the absolute value equation.
I I will represent absolute value
I y+3 I +5=2y
Would the solutions be 8=y and y=2/3?
To solve the absolute value equation |y + 3| + 5 = 2y, you can start by isolating the absolute value term:
|y + 3| = 2y - 5
Next, you can set up two separate equations, one for when the expression inside the absolute value is positive and one for when it is negative.
For positive:
y + 3 = 2y - 5
Simplifying this equation gives you:
y = 8
For negative:
-(y + 3) = 2y - 5
Simplifying this equation gives you:
- y - 3 = 2y - 5
- y - 2y = -5 + 3
-3y = -2
y = 2/3
So, the solutions to the absolute value equation |y + 3| + 5 = 2y are y = 8 and y = 2/3.