Question

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

7
1
−1
−7

Answer 1

To solve the equation

\[
\frac{3}{x - 4} = \frac{7}{x},
\]

we can cross-multiply to eliminate the fractions. This gives:

\[
3x = 7(x - 4).
\]

Now, distribute the 7 on the right side:

\[
3x = 7x - 28.
\]

Next, we will isolate \(x\) by moving all terms involving \(x\) to one side:

\[
3x - 7x = -28.
\]

This simplifies to:

\[
-4x = -28.
\]

Dividing both sides by \(-4\) gives:

\[
x = 7.
\]

To confirm that this solution is correct, we can substitute \(x = 7\) back into the original equation:

The left side becomes:

\[
\frac{3}{7 - 4} = \frac{3}{3} = 1,
\]

and the right side becomes:

\[
\frac{7}{7} = 1.
\]

Since both sides are equal, the solution is verified. Therefore, the final answer is:

\[
\boxed{7}.
\]