Question

What are the steps when solving: 14/7-x = 3

Answer 1

To solve the equation \( \frac{14}{7 - x} = 3 \), follow these steps:

1. **Eliminate the Fraction:**
Multiply both sides of the equation by \( 7 - x \) to get rid of the fraction. Ensure that \( 7 - x \neq 0 \) (which would make the denominator undefined).

\[
14 = 3(7 - x)
\]

2. **Distribute the Right Side:**
Distribute the 3 on the right side of the equation.

\[
14 = 21 - 3x
\]

3. **Rearrange the Equation:**
To isolate the term with \( x \), move \( 3x \) to the left side and \( 14 \) to the right side.

\[
3x = 21 - 14
\]

Simplifying the right side gives:

\[
3x = 7
\]

4. **Solve for \( x \):**
Divide both sides by 3.

\[
x = \frac{7}{3}
\]

5. **Conclusion:**
The solution to the equation \( \frac{14}{7 - x} = 3 \) is

\[
x = \frac{7}{3}
\]

You can substitute \( x = \frac{7}{3} \) back into the original equation to verify that it is correct.