X Marks the Spot
X. X is everywhere. It's the checkbox on the user agreement we never read. It marks railroad crossings and superhero uniforms. And, it's at the end of every pirate map. In all these examples, x stands for something. For example, on that pirate map, x is where you'll find the buried treasure. In algebra, x is sort of like a marker for treasure, if by treasure we mean a number. That's because x is a common variable. And, a variable is a symbol used to represent a number.
Here we're going to solve for x in linear equations. It's just like following a pirate map, where we follow the clues until we know where x is. Fortunately, with linear equation solving, you're much less likely to lose a leg or an eye. And, scurvy is very rare. First, let's do a quick review of what these equations are.
Linear Equations
A linear equation is simply an algebraic expression that represents a line. These equations commonly contain one or two variables, usually x or y. These are called first-degree equations because the variable's exponent is always one.
We won't see anything like x^2 or x^3. Those may get you lines like what you'd actually see on a pirate map. But, our pirate map has straight lines. It's much easier that way. You also won't see things like x times y, xover y or the square root of x. That's for pirates who travel through time and space.
Oh, and the linear equations we'll be solving here only have one variable, not two or more. I mean, if we had both x and y, how do we know which one has the treasure and which one is a trap? Pirates are big into traps.
Solving Linear Equations
As I mentioned before, to solve one of these equations, we're trying to solve for x. If you have x - 4 = 10, then 10 isn't where the treasure is. It's where x - 4 is. And, that's just not what we need.
To solve this equation, we need to get x alone on one side of the equation. Here, we do that by adding 4 to each side. That gets us x = 14. So, that's our treasure. I know that's a modest haul, but it was a basic equation.
For all of these equations, we'll always just do whatever we can to isolate x. If we have 2x = 6, we divide by 2 to get x = 3. Just keep your focus on x.