Let's solve the equation \( 4m + \frac{9}{3} = 7 - 2m \).

### Step 1: Simplify the fraction
Simplify \( \frac{9}{3} \) to get 3.

This gives us:
\[
4m + 3 = 7 - 2m
\]

### Step 2: Move all variable terms to one side
To move the \( -2m \) to the left side, add \( 2m \) to both sides:
\[
4m + 2m + 3 = 7
\]
This simplifies to:
\[
6m + 3 = 7
\]

### Step 3: Move constant terms to the other side
Subtract 3 from both sides to move the constants:
\[
6m = 7 - 3
\]
\[
6m = 4
\]

### Step 4: Solve for \( m \)
Divide both sides by 6:
\[
m = \frac{4}{6}
\]
Simplify the fraction:
\[
m = \frac{2}{3}
\]

So, the solution to the equation is:
\[
m = \frac{2}{3}
\]

Do you want further clarification or have any questions?

Here are five related questions:
1. How do you handle equations with fractions on both sides?
2. What is the general approach for solving linear equations?
3. Can you explain how to solve for a variable when both sides have terms with that variable?
4. How do you verify the solution to an equation?
5. What are the common mistakes to avoid when solving algebraic equations?

**Tip:** Always check your solution by substituting it back into the original equation!

Discover how to solve the linear equation 4m + 9/3 = 7 - 2m using a step-by-step solution. This solution covers fundamental algebraic concepts, including simplifying fractions and moving terms across the equation. Ideal for students in Grades 6-8.

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