To solve the equation \( 12 - (4y + 8) = 0.5(8y - 16) \), we need to simplify and solve for \( y \). Let's go through it step by step.

### Step 1: Distribute and simplify both sides
Expand the terms on both sides:

\[
12 - 4y - 8 = 0.5 \times 8y - 0.5 \times 16
\]

This simplifies to:

\[
4 - 4y = 4y - 8
\]

### Step 2: Move all terms involving \( y \) to one side
Add \( 4y \) to both sides to eliminate the \( -4y \) on the left:

\[
4 = 8y - 8
\]

### Step 3: Isolate the \( y \) term
Add \( 8 \) to both sides to isolate the term with \( y \):

\[
12 = 8y
\]

### Step 4: Solve for \( y \)
Divide both sides by 8:

\[
y = \frac{12}{8} = \frac{3}{2} = 1.5
\]

So, the solution is \( y = 1.5 \).

Would you like any further details or have any questions?

### Related Questions:
1. How do you solve linear equations with fractions?
2. What are some common mistakes when solving linear equations?
3. How do you check your solution to an equation?
4. Can linear equations have more than one solution?
5. How does the distributive property work in algebra?

### Tip:
Always simplify the equation as much as possible before trying to isolate the variable—it makes solving much easier!

Learn how to solve the equation 12 - (4y + 8) = 0.5(8y - 16) with a detailed step-by-step solution. This problem involves algebraic concepts like linear equations and the distributive property. Suitable for students in Grades 7-9.

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