One Step Equations


Equations have to be balanced with the same values on each side. If you do something to one side of an equation, you have to do the same thing to the other side of the equation. We can use this information to our advantage and solve for unknowns in equations.

Suppose we have the following basic equation:

x + 5 = 12

What if we subtract 5 from both sides?

x + 5 – 5 = 12 – 5
x = 7

This allows us to get rid of the “+5″ on the left side of the original equation, and get our variable x by itself. When we’re solving an equation, the goal is to get the variable by itself. We can check our answer, something we should always do, by substituting the value we got for the variable x into the original equation, and see if we get something that makes sense. So we have:

x + 5 = 12
7 + 5 = 12
12 = 12

And this obviously makes sense. So here’s another example. What if we have this equation:

x – 14 = 32

Our goal, if we are solving for x, is to get x by itself. To do this, we need to get rid of the -14. The opposite of subtracting 14 is adding 14, so we can add 14 to the left side of the equation to get rid of the -14. However, because we’re adding 14 to the left side, we have to add 14 to the right side to keep the equation balanced. With that line of reasoning, we have the following:

x – 14 = 32
x – 14 + 14 = 32 + 14
x = 32 + 14
x = 46

Once we solve for a variable, we always want to check our answer by plugging it back into the original equation. Here we go:

x – 14 = 32
46 – 14 = 32
32 = 32

And so we’re in good shape. Let’s look at some examples using multiplication and division.

16x = 64

Here we have x multiplied by 16. We would like to get x by itself, and the multiplication by 16 is what is standing in our way. The opposite of multiplying by 16 is dividing by 16, so we should divide the left side by 16. Since we’re dividing the left side by 16, we should divide the right side by 16 as well. That gives us:

16x = 64
16x/16 = 64/16
x = 4

Now, as always, we check our answer:

16x = 64
16(4) = 64
64 = 64

And we’re in good shape.