For the following equation:

To solve the equation, we can first clear the fractions by finding a common denominator. In this case, the common denominator for 3, 2, and 6 is 6. Rewriting the equation gives us:

.

Now, multiplying through by 6 to eliminate the denominator results in:

.

Subtracting from both sides leads to:

.

Finally, isolate to find .

To check our work, substitute back into the original equation. It’s always a good idea to verify solutions in math as it prevents potential calculation errors!

For extra fun, consider this: fractions and equations have been around for thousands of years, dating back to the ancient Egyptians who had their own unique methods. Understanding their evolution shows just how far we’ve come, especially with the tools available today, like calculators and software that can solve complex equations in seconds!

As for real-world applications, solving equations like this is essential in fields such as engineering, finance, and physics. Whether you’re calculating the trajectory of a rocket or balancing a budget, these skills help you make informed decisions. So the next time you encounter an equation, just remember it’s more than just numbers—it’s the language of problem-solving!