1/2 (6y - 20) - 5y = 12 - 2(-2y + 7) + 16

Answer 1

To solve the equation \( \frac{1}{2} (6y - 20) - 5y = 12 - 2(-2y + 7) + 16 \), we will simplify both sides.

Starting with the left side:

1. Distribute the \(\frac{1}{2}\): \[ \frac{1}{2}(6y - 20) = \frac{1}{2} \cdot 6y - \frac{1}{2} \cdot 20 = 3y - 10 \]

2. Substitute it back into the left side: \[ 3y - 10 - 5y = -2y - 10 \]

So the left side simplifies to: \[ -2y - 10 \]

Now, let’s simplify the right side:

1. Start with \( -2(-2y + 7) \): \[ -2(-2y + 7) = 4y - 14 \]

2. Substitute that into the right side: \[ 12 + 4y - 14 + 16 \]

3. Combine the constant terms: \[ 12 - 14 + 16 = 14 \]

Thus, the right side becomes: \[ 14 + 4y \]

Now, we can set the simplified left side equal to the simplified right side: \[ -2y - 10 = 14 + 4y \]

Next, we will solve for \(y\):

1. Add \(2y\) to both sides: \[ -10 = 14 + 6y \]

2. Subtract \(14\) from both sides: \[ -10 - 14 = 6y \implies -24 = 6y \]

3. Divide by \(6\): \[ y = \frac{-24}{6} = -4 \]

The solution is: \[ \boxed{-4} \]