In this video, we will be learning how to solve for x (or another variable) in complex algebraic equations using inverse operations. After you finish this lesson, view all of our Pre-Algebra and Algebra lessons and practice problems.

## Example of Solving a Multi-Step Algebraic Equation

Subtract 2 from both sides

Divide by 5 on both sides

Subtract 4 on both sides

### Example 1

First, distribute to the terms inside the parenthesis

Then, subtract from both sides

divide from both sides

Now, we have:

### Example 2

First, distribute to the terms inside the parenthesis

Then, add from both sides

divide from both sides

Now, we have:

Another way of doing this problem:

Distribute the 5 to the x and the 4

Simplify using addition

Subtract 22 from both sides

Divide by 5 on each side

## Video-Lesson Transcript

Let’s get into solving complex algebraic equations. This involves more than one operation.

To review, order of operations or PEMDAS, we have .

PEMDAS is an acronym which stands for

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Let’s evaluate .

So we’ll have .

In solving algebraic equations, we don’t have all whole numbers. Instead, we have variables in it.

So, we may have .

From our example, we already know that .

But let’s try solving this algebraically.

We just have to do few steps to solve this.

1. Simplify both sides of the equations, if possible.

2. If there’s terms on both sides, we have to get all the terms on one side. You can have it on the left side or on the right side, whichever you prefer.

3. Reverse PEMDAS. We’re going to do the order of operations backward using inverse operations.

4. Our goal is to isolate the variable .

Going back to , let’s do the steps above.

1. Simplify – This is the simplest it can get.

2. All term on one side – There’s just one and it’s on the left.

3. Now, let’s do the reverse PEMDAS using inverse operations.

Let’s subtract on both sides of the equation.

We’ll have .

4. Isolate

Here we have to divide both sides by .

And we’ll have .

Let’s do another example.

We have

So, let’s start off by adding on both sides of the equation.

We’ll come up with

Then, we multiply on both sides.

The answer is

Let’s have one more example. I’ll show you how to solve this using two different ways.

We have

First method of solving is this:

Let’s subtract on both sides of the equation.

We’ll have

Then, we have to divide both sides by

We’ll come up with

Then, to isolate we have to subtract on both sides

Our final answer is

So now let’s move on to the second method of solving the same equation.

The second method is to simplify the equation as much as we can.

Let’s start off by distributing into the equation in the parenthesis –

So let’s do it!

and

We’ll have

Now, we can combine like terms to simplify further

Then we have to do the reverse PEMDAS.

Let’s subtract on both sides

We’ll come up with

Now, let’s do the inverse of multiplication which is division.

Divide both sides by

Our final answer is

Both methods gave us the same answer .

To sum up, no matter how complex our algebraic equation is, we can do reverse PEMDAS or inverse order of operations to isolate the .