https://r2.erweima.ai/mathbot/image/172671108113860e1uegl.jpg

The equation from the image is:

\[
4(6 - y) - y = 8(3 + y) - 13
\]

Let's solve for \( y \).

### Step 1: Distribute the terms
Expand both sides of the equation:
\[
4 \times 6 - 4 \times y - y = 8 \times 3 + 8 \times y - 13
\]
This simplifies to:
\[
24 - 4y - y = 24 + 8y - 13
\]
\[
24 - 5y = 24 + 8y - 13
\]

### Step 2: Simplify both sides
Simplify the constants on the right-hand side:
\[
24 - 5y = 24 + 8y - 13
\]
\[
24 - 5y = 11 + 8y
\]

### Step 3: Move variables to one side
Move all terms involving \( y \) to one side and constants to the other side:
\[
24 - 11 = 8y + 5y
\]
\[
13 = 13y
\]

### Step 4: Solve for \( y \)
Divide both sides by 13:
\[
y = 1
\]

The value of \( y \) is \( \boxed{1} \).

Would you like a more detailed explanation of any step? 

Here are five related questions:
1. How would you solve a similar equation with fractions?
2. What if the equation included absolute values?
3. How can we check if the solution \( y = 1 \) is correct?
4. Can this method be applied to inequalities?
5. How does distributing affect the structure of an equation?

**Tip:** Always simplify both sides of an equation before moving terms around. This makes solving much more straightforward!

Halla el valor de 'y' si: 4(6 - y) - y = 8(3 + y) - 13

Learn how to solve the linear equation 4(6 - y) - y = 8(3 + y) - 13. This problem involves key algebraic concepts like the distributive property, combining like terms, and solving for a variable. Suitable for students in Grades 8-10.

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