Find the solution set of the equation four divided by 𝑥 equals 𝑥 divided by nine.
If we have a fraction equal to another fraction, we can cross-multiply and solve. So we begin by taking 𝑥 times 𝑥 and then setting it equal to four times nine. 𝑥 times 𝑥 is equal to 𝑥 squared, and four times nine is equal to 36.
Now in order to solve for 𝑥, we need to square-root both sides of the equation. The square root of 𝑥 squared is 𝑥, and the square root of 36 is positive six. But it’s also equal to negative six, because six squared is equal to 36 and negative six squared is equal to 36. Therefore, our solution set will be six and negative six.