\( 10 x-1=15-6 x \)

First, let's solve the equation \( 10x - 1 = 15 - 6x \). Start by getting all the terms involving \( x \) on one side and the constants on the other. Add \( 6x \) to both sides: \( 10x + 6x - 1 = 15 \) This simplifies to: \( 16x - 1 = 15 \) Next, add 1 to both sides: \( 16x = 16 \) Finally, divide both sides by 16: \( x = 1 \) So, the solution is \( x = 1 \). Solving systems of equations has been a critical part of mathematics for centuries. From Isaac Newton’s work in calculus to today's advanced algorithms in computer science, mastering equations such as this paves the way for future explorations in various fields, including engineering, physics, and economics. In real-world applications, being able to decipher and solve equations like this is crucial. Whether budgeting for a project, determining a workout schedule, or planning a road trip, understanding how to manipulate variables helps you make better decisions and optimize outcomes based on different constraints and goals.