Solve for x: 3 over quantity x minus 4 equals 7 over x

 7
 1
 −1
 −7

To solve the equation \(\frac{3}{x - 4} = \frac{7}{x}\), follow these steps:

1. **Cross Multiply:**
   \[
   3x = 7(x - 4)
   \]

2. **Distribute on the right-hand side:**
   \[
   3x = 7x - 28
   \]

3. **Isolate the \(x\) terms:**
   Subtract \(7x\) from both sides:
   \[
   3x - 7x = -28
   \]
   \[
   -4x = -28
   \]

4. **Solve for \(x\):**
   Divide both sides by \(-4\):
   \[
   x = \frac{-28}{-4} = 7
   \]

The solution is \(x = 7\).

Would you like more details or have any questions about this? Here are some related problems you might find helpful:

1. Solve for \(x\): \(\frac{5}{x-2} = \frac{10}{x}\)
2. Solve for \(x\): \(\frac{4}{x+3} = \frac{8}{x-1}\)
3. Solve for \(x\): \(\frac{2x+1}{x-3} = \frac{4x-2}{x+5}\)
4. Solve for \(x\): \(\frac{6}{x+2} = \frac{9}{x-4}\)
5. Solve for \(x\): \(\frac{3x-4}{x+1} = \frac{7x+2}{x-2}\)
6. Solve for \(x\): \(\frac{5}{x} = \frac{20}{x-6}\)
7. Solve for \(x\): \(\frac{8x+3}{x-5} = \frac{16x-6}{x+7}\)
8. Solve for \(x\): \(\frac{7}{x+4} = \frac{14}{x-2}\)

**Tip:** When dealing with fractions in equations, cross-multiplication is a powerful technique to eliminate the fractions and simplify the equation.

Learn how to solve the equation 3/(x - 4) = 7/x step-by-step. This problem involves algebraic equations with fractions and requires cross multiplication to find the solution. Suitable for Grades 7-9.

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