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The given equation is:

\[
6x + 7y = 4x + 4y
\]

We are asked to find the missing value for \( x \) when \( y = -4 \).

### Step 1: Simplify the equation
First, let's move all terms involving \( x \) and \( y \) to one side of the equation:

\[
6x + 7y - 4x - 4y = 0
\]

Simplifying further:

\[
(6x - 4x) + (7y - 4y) = 0
\]

\[
2x + 3y = 0
\]

### Step 2: Substitute \( y = -4 \) into the equation
Now, we substitute \( y = -4 \) into the equation:

\[
2x + 3(-4) = 0
\]

\[
2x - 12 = 0
\]

### Step 3: Solve for \( x \)
Now, solve for \( x \):

\[
2x = 12
\]

\[
x = 6
\]

Thus, the missing value is \( x = 6 \).

### Final answer:
The solution to the equation is \( (6, -4) \).

Let me know if you would like more details, or if you have any questions!

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Here are five related questions you might want to explore:
1. How would the solution change if \( y = 0 \)?
2. Can you express the equation \( 2x + 3y = 0 \) in terms of \( y \) as a function of \( x \)?
3. What is the general solution to the equation \( 2x + 3y = 0 \)?
4. How would you graph the equation \( 2x + 3y = 0 \) in the coordinate plane?
5. How does the substitution method work for solving systems of equations?

**Tip:** Always simplify equations by combining like terms first—it makes solving for variables much easier.

Complete the missing value in the solution to the equation 6x + 7y = 4x + 4y, where y = -4.

Learn how to solve the linear equation 6x + 7y = 4x + 4y by simplifying terms and substituting y = -4. This problem covers key algebra concepts and is suitable for students in Grades 6-8.

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