To solve the equation \(\frac{x+1}{3} = \frac{x-5}{4}\), follow these steps:

1. **Eliminate the fractions** by multiplying both sides of the equation by the least common denominator (LCD) of the fractions. The LCD of 3 and 4 is 12.

\[
12 \cdot \frac{x+1}{3} = 12 \cdot \frac{x-5}{4}
\]

2. **Simplify the equation**:

\[
4(x + 1) = 3(x - 5)
\]

3. **Distribute** the numbers on both sides:

\[
4x + 4 = 3x - 15
\]

4. **Isolate the variable \(x\)** by subtracting \(3x\) from both sides:

\[
4x - 3x + 4 = -15
\]

\[
x + 4 = -15
\]

5. **Solve for \(x\)** by subtracting 4 from both sides:

\[
x = -19
\]

So, the solution is \(x = -19\).

Would you like more details or have any questions? 

Here are 8 related questions for further exploration:

1. How can you check the solution of the equation \(\frac{x+1}{3} = \frac{x-5}{4}\)?
2. What is the significance of finding the least common denominator in equations with fractions?
3. How would the solution change if the equation was \(\frac{2x+1}{3} = \frac{x-5}{4}\)?
4. Can you solve the equation \(\frac{x+3}{2} = \frac{2x-4}{3}\)?
5. How does the solution process differ if the equation involves decimals instead of fractions?
6. What would the equation look like if it had a different variable instead of \(x\)?
7. How can you solve the equation if both sides are multiplied by a different number instead of the LCD?
8. Can you solve the equation \(\frac{x+1}{3} + \frac{x-5}{4} = 0\)?

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

Learn how to solve the equation (x+1)/3 = (x-5)/4 with a detailed step-by-step solution. This problem involves equations with fractions, requiring methods to eliminate fractions and isolate the variable x. Suitable for students in Grades 7-9.

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