Let's solve the equation \( \frac{2x - 5}{x + 4} = 1 \).

### Step 1: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by \( x + 4 \):

\[
(x + 4) \cdot \frac{2x - 5}{x + 4} = 1 \cdot (x + 4)
\]

This simplifies to:

\[
2x - 5 = x + 4
\]

### Step 2: Solve for \( x \)
Now, we'll isolate \( x \) on one side of the equation:

\[
2x - x = 4 + 5
\]

Simplify:

\[
x = 9
\]

### Step 3: Verify the solution
Substitute \( x = 9 \) back into the original equation to check:

\[
\frac{2(9) - 5}{9 + 4} = \frac{18 - 5}{13} = \frac{13}{13} = 1
\]

Since the left-hand side equals the right-hand side, the solution is correct.

### Final Answer
The solution is \( \boxed{9} \).

Would you like details on any specific step or have any questions?

Here are some related questions you might find interesting:

1. How do you solve equations with variables on both sides?
2. What are the steps to solving rational equations?
3. Can you show me how to solve a quadratic equation?
4. How do you handle equations where the variable is in the denominator?
5. What are some common mistakes to avoid when solving equations?

**Tip:** Always check your solution by substituting it back into the original equation. This helps confirm that your answer is correct.

Learn how to solve the equation 2x - 5 / (x + 4) = 1 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving equations with fractions. Suitable for students in Grades 7-9.

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