Algebra can sometimes feel like a puzzle, with each piece needing to fit just right. Take the equation x - 4x = 5, for instance. At first glance, it might seem daunting, but let’s break it down together.
When we look at this expression closely, we see that it's simply asking us to combine like terms. The left side of the equation features two instances of 'x': one positive and one negative (specifically -4x). So how do we simplify this?
We start by rewriting it as follows:
(1) x - (4)x = 5.
This gives us (-3)x = 5 after combining those terms—an important step in solving any algebraic equation. Now we're getting somewhere! To isolate 'x', we'll divide both sides by -3:
(2) x = 5 / (-3).
And there you have it! Simplifying further leads us to: x = -5/3.
It’s fascinating how such a simple manipulation reveals an answer that may not be immediately obvious. This process highlights not only the beauty of algebra but also its logical structure—a series of steps leading from confusion to clarity.
So next time you encounter an equation like this one, remember: every complex problem has a solution waiting patiently behind layers of numbers and symbols.