Solving Equations

Solving algebra equations is difficult for many. If you struggle with algebra solving equations can be improved using this lesson and practice.

Longer equations

Believe it or not, you now have the tools to simplify many expressions, even complicated-looking ones like this:

3x - 24 ⋅ 2 = 8x + 2

This might look more difficult than the problems you solved on the last page, but you'll use the exact same skills to solve this one. The major difference between this expression and the others you solved is that this one has a variable and at least one number on both sides of the equals sign—so you'll have to do a bit more cancelling out.

You'll also have to choose whether you want the variable on the left or the right side of the equals sign in your simplified expression. It doesn't really matter—the answer will be the same either way—but depending on the problem, you might find that the math feels easier one way than another. No matter what, though, your simplified equation should have only a variable on one side of the equation and only a number on the other.

Let's try the problem from the top of the page: 3x - 24 ⋅ 2 = 8x + 2.

First, we'll want to handle what we can with the order of operations. It looks like all we can do is multiply -24 ⋅ 2. Everything else involves adding or subtracting unlike terms: -24 ⋅ 2 is -48.

3x -24 ⋅ 2 = 8x + 2

Let's try to get x on the left side of the equals sign and the number on the right. We'll start by cancelling out -48 on the left. We can do this by adding 48 to both sides. -48 + 48 is 0, and 2 + 48 is 50.

3x-48=8x+ 2
+ 48+ 48

Because we decided that x will be on the left side, we have to get rid of 8x on the right. We can do this by subtracting 8x from both sides. 8x - 8x is 0, and 3x - 8x is -5x.

3x=8x+ 50
- 8x- 8x

Now all that's left to do is to get rid of the -5 in -5x. Because -5x is a way of writing -5 ⋅ x, we can cancel it by dividing both sides by -5. -5x / -5 is x, and 50 / -5 is 10.

-5x=50
-5-5

We're done! x is equal to -10.

x = -10

As you can see, simplifying this equation really wasn't much more complicated than simplifying any of the other equations in this lesson—it just took a little longer.

Watch the video below to see this example problem solved.

Practice!

Now it's your turn. Try simplifying these longer expressions.

Problem 1

Solve for i.

-46 -2i = 42 + 7i ⋅ 6

Problem 2

Solve for j.

90j / 5 + 22 = 140 + j

Problem 3

Solve for k. (Hint: your final answer will be a fraction.)

3 + (3k + 6k) = 3k + 5

Answers

  1. i = -2
  2. j = 8
  3. k = 1/3