Question
(SW) Solve the following equation for the variable k 9/k-7=6/k
Answers
GPT-4o mini
To solve the equation \(\frac{9}{k} - 7 = \frac{6}{k}\), we start by eliminating the fractions. First, we can multiply both sides of the equation by \(k\) (assuming \(k \neq 0\)):
\[
k \cdot \left(\frac{9}{k} - 7\right) = k \cdot \frac{6}{k}
\]
This simplifies to:
\[
9 - 7k = 6
\]
Next, we can isolate \(k\) by moving terms around. First, move \(9\) to the other side:
\[
-7k = 6 - 9
\]
This simplifies to:
\[
-7k = -3
\]
Now, divide both sides by \(-7\):
\[
k = \frac{-3}{-7} = \frac{3}{7}
\]
Thus, the solution for \(k\) is:
\[
\boxed{\frac{3}{7}}
\]
\[
k \cdot \left(\frac{9}{k} - 7\right) = k \cdot \frac{6}{k}
\]
This simplifies to:
\[
9 - 7k = 6
\]
Next, we can isolate \(k\) by moving terms around. First, move \(9\) to the other side:
\[
-7k = 6 - 9
\]
This simplifies to:
\[
-7k = -3
\]
Now, divide both sides by \(-7\):
\[
k = \frac{-3}{-7} = \frac{3}{7}
\]
Thus, the solution for \(k\) is:
\[
\boxed{\frac{3}{7}}
\]