What is the solution to the following equation? \( \frac{2}{3} x-5=7 \)

To solve the equation \( \frac{2}{3} x - 5 = 7 \), start by isolating the term with \( x \). First, add 5 to both sides to get \( \frac{2}{3} x = 12 \). Next, multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \). This gives you \( x = 12 \times \frac{3}{2} = 18 \). So, the solution is \( x = 18 \). Did you know that the concept of linear equations dates back to ancient civilizations? Egyptians and Babylonians used similar methods in solving for unknowns, long before algebra was formally introduced. It's fascinating how these foundational principles have shaped modern mathematics! In real-life situations, linear equations appear in various fields such as finance, engineering, and science. For instance, you might use them to calculate budgets, analyze supply and demand in economics, or determine the trajectory of a moving object in physics. Mastering these equations can unlock numerous practical applications!