https://file.aiquickdraw.com/mathbot/file/17283315903158n8zl0m7.jpg

The equation provided is:

\[
\frac{4m + 9}{3} = 7 - 2m
\]

To solve this step by step:

### Step 1: Eliminate the denominator
Multiply both sides of the equation by 3 to eliminate the denominator:

\[
4m + 9 = 3(7 - 2m)
\]

### Step 2: Expand the right-hand side
Now expand the right-hand side:

\[
4m + 9 = 21 - 6m
\]

### Step 3: Collect like terms
Add \(6m\) to both sides to bring all the terms involving \(m\) to one side:

\[
4m + 6m + 9 = 21
\]

This simplifies to:

\[
10m + 9 = 21
\]

### Step 4: Isolate the term with \(m\)
Subtract 9 from both sides:

\[
10m = 12
\]

### Step 5: Solve for \(m\)
Divide both sides by 10:

\[
m = \frac{12}{10} = 1.2
\]

Thus, the solution is:

\[
m = 1.2
\]

Would you like more details or have any questions?

### Related questions:
1. How can you verify if \(m = 1.2\) is correct?
2. What happens if we had a different constant instead of 9 in the original equation?
3. How would this change if \(4m\) was replaced with another variable?
4. How can we graph both sides of the equation to visualize the solution?
5. How does the solution process differ if the equation had a quadratic term?

### Tip:
Always check your solution by substituting it back into the original equation to verify that both sides are equal.

Solve (4m + 9) / 3 = 7 - 2m. Show clear algebraic working.

Learn how to solve the linear equation (4m + 9) / 3 = 7 - 2m with a detailed step-by-step algebraic solution. This problem covers fundamental algebraic concepts, including balancing equations and isolating variables. Suitable for students in Grades 8-10.

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