Let's solve the equation \(-4 + \frac{2}{3}m = 3 + \frac{7}{9}m - \frac{8}{9}m\).

### Step 1: Simplify the equation
First, combine like terms on the right side of the equation.

The right side is:
\[
\frac{7}{9}m - \frac{8}{9}m = \frac{7 - 8}{9}m = -\frac{1}{9}m
\]
So the equation becomes:
\[
-4 + \frac{2}{3}m = 3 - \frac{1}{9}m
\]

### Step 2: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD) for \(\frac{2}{3}\) and \(\frac{1}{9}\). The LCD is 9.

Multiply the entire equation by 9 to eliminate the fractions:
\[
9(-4) + 9\left(\frac{2}{3}m\right) = 9(3) + 9\left(-\frac{1}{9}m\right)
\]
This simplifies to:
\[
-36 + 6m = 27 - 1m
\]

### Step 3: Combine like terms
Now, let's move the terms involving \(m\) to one side and constants to the other:
\[
6m + 1m = 27 + 36
\]
This simplifies to:
\[
7m = 63
\]

### Step 4: Solve for \(m\)
Now, divide both sides by 7 to solve for \(m\):
\[
m = \frac{63}{7} = 9
\]

### Final Answer:
\[
m = 9
\]

Would you like more details or have any questions?

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Here are some related questions:
1. How do you solve equations with multiple fractions?
2. What happens if the LCD is not easily found?
3. Can you explain how to check the solution?
4. What if there were decimals instead of fractions?
5. How would you solve this equation graphically?
6. What is the importance of isolating the variable?
7. How can you verify the solution of an equation?
8. What if the equation involved more complex fractions?

**Tip:** Always simplify both sides of the equation as much as possible before solving.

Learn how to solve the equation -4 + 2/3m = 3 + 7/9m - 8/9m with a detailed step-by-step solution. This problem covers solving equations involving fractions, finding the LCD (Least Common Denominator), and simplifying expressions. Suitable for students in Grades 7-9.

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