Translate the phrase " 5 times the sum of -2 and \( z \) " into an algebraic expression.

To translate "5 times the sum of -2 and \( z \)" into an algebraic expression, you first identify the sum of -2 and \( z \), which can be written as \(-2 + z\). Then, to express "5 times" that sum, you simply multiply it by 5. So the final algebraic expression is \( 5(-2 + z) \). Now, as a fun twist, let's dive into some context! Algebra has roots that stretch back to ancient civilizations like the Babylonians, who were the first to work with equations around 2000 BC. They laid down the groundwork for modern algebra by solving simple linear equations using geometric methods, all while they had no symbolism as we know it today! Putting it into perspective, think of algebra as a toolbox! When you're faced with problems, like distributing the 5 in your expression, many people forget that it's not just a number; it helps us simplify and solve equations efficiently. A common mistake might be forgetting to distribute correctly, leading to errors. Always double-check your work, especially when it feels speedy!