One of the main and very important basics of algebra is solving an equation for an unknown value. This fundamental method is used in all types of math problems and is necessary even later in the toughest and most advanced math courses! Don’t worry though. We are going to start simple and one step at a time.

In math, there are such things known as inverse operations. These are operations that do the opposite action. They basically “undo” each other. An operation is something like addition or subtraction and so forth.

So, let’s see. What would be the inverse or opposite operation as addition? It would be subtraction! How about the inverse or opposite of multiplication? This would be division. These are the inverse operations that you will need for one-step equations.

Inverse Operations

Addition ↔ Subtraction

Multiplication ↔ Division

We have to use these inverse operations to cancel out or “undo” operations so that we can solve a problem with an unknown. Let’s look at a few examples.

Example 1:

Solve for x.
\({\rm{x }} + {\rm{ 5 }} = {\rm{ 12}}\)

We want to get x by itself. The inverse operation that will undo the “add 5” would be to subtract 5. We must do this to both sides of the equation to keep it balanced.

x + 5 = 12

    - 5      -5

x = 7

You can check your answers by plugging the value back in for x. Let’s try.

x + 5 = 12

7 + 5 = 12

12 = 12          It works!

Example 2:

Solve for x.
\({\rm{5x }} = {\rm{ 2}}0\)

The left side of the equation is read as “5 times x,” so this is multiplication. That means we must cancel out the 5 by dividing both sides by 5. This will get x by itself.

5x = 20

5        5

 x = 4

Example 3:

Solve for b.
\(\frac{b}{7} = 20\)

This one always seems to stump some people. You have to ask yourself, what is the 7 doing down there? Is it adding, subtracting, multiplying or dividing? It’s dividing! So, the inverse operation would be multiplication. We must multiply both sides by 7.

\(\frac{b}{7} \bullet 7 = 20 \bullet 7\)

\(b = 140\)

Let’s look at one more tricky example.

Example 4:

Solve the equation.
\(39 = m - ( - 14)\)

When you have two signs in a row (minus, minus) it is always confusing, so let’s change it to one sign. When you subtract a negative number, it’s the same as adding the number, so we can change this to:

\(39 = m + 14\)

Now, we can see that we must subtract 14 from both sides to solve.

 39 = m + 14

-14         -14

25 = m