6. \( 3(2 d-5)=-3 \)

To solve the equation \( 3(2d-5)=-3 \), start by distributing the 3 on the left side. This gives you \( 6d - 15 = -3 \). Next, add 15 to both sides to isolate the term with \( d \): \( 6d = 12 \). Finally, divide both sides by 6 to find \( d \): \( d = 2 \). So, the solution to the equation is \( d = 2 \). You just solved a linear equation! Linear equations have a rich history, with roots stretching back to ancient civilizations. The Babylonians were among the first to use them around 2000 BC, laying the groundwork for modern algebra. Isn’t it fascinating how such mathematical concepts have stood the test of time? In the real world, linear equations are used in various fields like economics, physics, and engineering. For instance, businesses often use these equations to analyze costs and profits, helping minimize expenses while maximizing revenues. Understanding how to manipulate and solve equations allows professionals to make data-informed decisions that can significantly impact their success!