We can solve the equation step by step:

Given equation:

\[
3x + 2y - 4 = 2(5 - y)
\]

1. **Expand the right side**:

\[
3x + 2y - 4 = 10 - 2y
\]

2. **Move all terms involving \( y \) to one side**:

\[
3x + 2y + 2y = 10 + 4
\]

This simplifies to:

\[
3x + 4y = 14
\]

Now, we have the simplified equation:

\[
3x + 4y = 14
\]

This is a linear equation in two variables, \( x \) and \( y \). To solve further, you would either need a value for \( x \) or \( y \), or another equation to solve the system.

Would you like to solve for one variable or work on something else related to this equation?

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**Related questions:**
1. How do you solve a system of two linear equations?
2. What is the method of substitution in solving equations?
3. Can you graph the equation \( 3x + 4y = 14 \)?
4. What are the real-world applications of linear equations like this?
5. How do you determine if an equation has no solution, one solution, or infinitely many solutions?

**Tip:** Always simplify both sides of an equation as early as possible to reduce complexity in solving.

Learn step-by-step how to solve the linear equation 3x + 2y - 4 = 2(5 - y). This algebra problem involves expanding expressions, simplifying terms, and isolating variables. Suitable for students in Grades 8-10, this problem covers key concepts like linear equations and algebraic manipulation.

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