Algebraic Equations

In this example, we are given an equation. X plus one plus two x is equal to x plus eleven.

Sometimes when we see an equation written with just numbers and letters, it can feel overwhelming or confusing. But when we represent it with objects, like cups for our unknown values, x, and cubes for our known values, it's easier to understand.

So let's set it up on the equations mat. On the left side of the equation, we have one x and then another two x's. That means we need three cups, and there is one cube. On the right side of the equation, let's use one cup to represent the x and eleven cubes.

We can use trial and error to find the value of each cup. If each cup has a value of one, the left side equals four, and the right side is equal to twelve. That's a pretty big difference.

Let's try adding some more cubes to each cup. I'm going to add three more cubes to each cup. Now each one has a value of four. This makes the left side of the equation equal thirteen, and the right side equals fifteen. We are not perfectly balanced yet, but we are getting closer.

Let's try adding one more cube to each cup. When each cup equals five, the left side is equal to sixteen, and the right side is also sixteen.

We have an answer. The value of each cup is five.

We can check this mathematically by substituting five in for x. Five plus one plus five plus five equals five plus eleven. Sixteen equals sixteen. It checks out.

And if you find yourself in a situation where you are asked to solve this type of problem using pencil and paper, no worries. You can still do it. Draw circles to represent our unknown values, x, and squares to represent our known number values. Then use the trial and error strategy, testing different values until both sides are balanced.

And now, you're ready to begin solving equations that use variables like x.