Let's solve the equation for \( x \), \( y \), and \( z \) in terms of each other. The equation is:

\[
2x + 4y + 6z + 3000 = 9125
\]

### Step 1: Simplify the equation
Subtract 3000 from both sides:

\[
2x + 4y + 6z = 6125
\]

### Step 2: Factor out the common factor on the left side
Notice that 2 is a common factor for all the terms on the left side:

\[
2(x + 2y + 3z) = 6125
\]

### Step 3: Divide both sides by 2 to solve for \( x + 2y + 3z \)

\[
x + 2y + 3z = \frac{6125}{2} = 3062.5
\]

### Final result:
The equation simplifies to:

\[
x + 2y + 3z = 3062.5
\]

This expression shows the relationship between \( x \), \( y \), and \( z \). Without additional equations, we cannot determine unique values for \( x \), \( y \), and \( z \).

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Would you like more details, or do you have any questions?

Here are some related questions:
1. How would you solve for one variable given the other two?
2. What happens if we add another equation to create a system of equations?
3. How can we interpret the solution geometrically?
4. Can this equation be solved using matrix methods?
5. How would the solution change if the constants on the right side were different?

**Tip:** When dealing with equations involving multiple variables, additional equations are necessary to solve for individual variable values.

Learn how to solve the linear equation 2x + 4y + 6z + 3000 = 9125 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations with multiple variables. Suitable for students in Grades 7-9.

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