https://file.aiquickdraw.com/mathbot/file/1725553583855v4tby4m9.jpg

The image contains a mathematical problem involving fractions. Let's go through it step-by-step to solve it.

### Problem Analysis:

Given the expressions:
\[
\frac{m - 2}{4} = \frac{8 - m}{5}
\]

We need to find the value of \(m\).

### Solution:

To solve this, let's clear the fractions by finding a common denominator or cross-multiplying:

1. **Cross-multiplication**:
   \[
   5(m - 2) = 4(8 - m)
   \]

2. **Expand both sides**:
   \[
   5m - 10 = 32 - 4m
   \]

3. **Combine like terms**:
   \[
   5m + 4m = 32 + 10
   \]

   \[
   9m = 42
   \]

4. **Solve for \(m\)**:
   \[
   m = \frac{42}{9} = \frac{14}{3}
   \]

So, the solution to the equation is:
\[
m = \frac{14}{3}
\]

Would you like further details or have any questions?

### Related Questions:

1. How do you solve an equation involving fractions using a different method?
2. What are the steps to simplify a fraction?
3. How do you solve equations with multiple variables?
4. Can you show how to solve similar equations using graphing methods?
5. What are some real-life applications of solving equations with fractions?

### Tip:

When solving equations involving fractions, clearing the fractions early by multiplying through by the least common denominator (LCD) can simplify your work and reduce errors.

Learn how to solve an algebraic equation involving fractions: (m - 2)/4 = (8 - m)/5. This step-by-step solution explains the process of cross-multiplication and combining like terms, suitable for students in Grades 6-8.

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