Solve \( \frac{2}{5} x=6 \) \( x=\square \)

To solve the equation \( \frac{2}{5} x=6 \), you need to isolate \( x \). Start by multiplying both sides of the equation by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \): \[ x = 6 \cdot \frac{5}{2} \] Now, calculate the right side: \[ x = 6 \cdot 2.5 = 15 \] So, the final answer is \( x = 15 \). Now you've got your solution! This shows how a simple manipulation of fractions can lead you to the answer. If you were to apply this kind of equation in real life, think about budgeting. If you know you have to set aside \( \frac{2}{5} \) of your monthly spending for essentials, and you find that amount totals $6, you'd quickly realize your total budget for the month would be $15! Always helps to find the bigger picture, doesn't it? When working with fractions, one common mistake is forgetting to multiply both sides by the same value. It's an easy slip—like thinking you can skip leg day at the gym! Just remember to treat both sides equally, and you’ll build strong math muscles!