Let's solve the equation \( 2 = \frac{x + 7}{x - 5} \).

### Step 1: Multiply both sides by \( x - 5 \) to eliminate the fraction:
\[
2(x - 5) = x + 7
\]

### Step 2: Distribute the 2 on the left side:
\[
2x - 10 = x + 7
\]

### Step 3: Move all terms involving \( x \) to one side of the equation and the constants to the other side:
\[
2x - x = 7 + 10
\]
\[
x = 17
\]

### Step 4: Verify the solution by substituting \( x = 17 \) back into the original equation:
\[
2 = \frac{17 + 7}{17 - 5}
\]
\[
2 = \frac{24}{12}
\]
\[
2 = 2
\]
Since both sides are equal, the solution is correct.

### Final Answer:
\[
x = 17
\]

Would you like more details, or do you have any questions? Here are some related questions for further practice:

1. Solve \( \frac{3x + 2}{x - 4} = 5 \).
2. Solve \( \frac{x - 2}{x + 3} = 1 \).
3. Solve \( \frac{x + 5}{2x - 7} = 3 \).
4. Solve \( 4 = \frac{2x - 1}{x + 6} \).
5. Solve \( \frac{5x + 4}{x - 1} = 6 \).

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 2 = (x + 7) / (x - 5) with a detailed step-by-step solution. This problem covers algebraic equations involving rational expressions. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation