Solving Multi-Step Equations

Contributor: Mason Smith. Lesson ID: 11186

Solve for x. Solve for y. That would be easy if numbers weren't involved! You'll learn the steps (and enjoy some snacks as well), and even master fractions, with online and pencil-and-paper practice!

categories

High School, Middle School

subject
Math
learning style
Visual
personality style
Lion
Grade Level
Middle School (6-8), High School (9-12)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Q: How do equations get into shape?

A: They do multi-step aerobics!

Solving multiple-step equations is the next huge hurdle in algebra that takes a lot of careful work in order to be mastered.

The most important idea is to get, or "find," x, but how do we do that? What if it is a y? How do I get that all by its lonesome on one side of the equation?

Instead of thinking of the letter as some complicated variable, I want you to think of it as a blob, a Kit Kat, a gummy bear, a question mark, or whatever your favorite candy may be!

We are going to tackle the three biggest parts of solving multi-step equations: solving ones with two-steps, ones with fractions, and ones with multiple steps.

Now, write down on a piece of paper the equation (remember: "equation" means it has an equal sign!) 10 = 6 + 2x and cover up the "x" with your favorite candy, like maybe a gummy bear. You can't have that piece of candy quite yet — not until you get it all by itself! You don't want any numbers getting on your gummy bear, do you? So to get it by itself, the most important thing to do is remember to balance both sides of the equation!

  • What do you think we should get rid of first? How about all the numbers not connected to our gummy bear? That's definitely the easier way!
  • To slide the 6 over to the same side as the 10, we have to cancel it out! Since it is a positive number we have to add the opposite, -6, so the 6 - 6 on the right side just become 0. Don't forget to balance out the equation!
  • We now have 10 – 6 = 2(gummy), which I think we can make a little bit smaller, so let's squeeze the 10 and the -6 together to make 4.
  • Now that we only have 4 = 2(gummy), how are we going to get that gummy bear by himself? We have to get rid of that 2! Since it is right next to the gummy bear, that means we have to do the opposite of multiplication, which is? Division!
  • So divide both sides by 2 and that just leaves us 2 = (gummy), and since it is all by its lonesome, not only do you get to eat that gummy bear, you also get to gold-star that equation because you solved for the variable!

Now that we have solved a super-easy equation, let's kick it up a notch and throw in everybody's favorite: fractions!

To start, write down the equation below on a piece of paper and cover "p" with a gummy:
                         

  • Do you know what's the first thing I do whenever I have fractions? I get rid of them! They are stinky, smelly, and don't play nice!
  • So, to get rid of them, what are you going to do? Multiply everything by the least common denominator! Here the LCD is 15, so let's multiply everything by 15!
  • *Trick* If you forget to multiply everything, I suggest putting a pair of parentheses around both sides of the equal sign before you multiply!
  • So, when we multiply 
                   
    we get 
                    
    but we can simplify that, right?
  • After simplifying the fractions, we have gummy - 3 = 6.
  • I bet you know how to solve from here! Try and solve it from here, and when you are ready, look at the next dot!
  • So did you get gummy = 9? If not, then go back to the equation gummy - 3 = 6 and add 3 to both sides and you are good to eat that delicious gummy bear!

Sometimes, before we can solve for a variable "x," we have to first find all the x's and put them together! Take 6x - 8x + 3 = 13; let's just put the 6x and the -8x together and we get -2x + 3 = 13 Now all we have to do is solve! Try it on your own before checking the answer (no peeking!).

Answer: x, or gummy bear, = -5

How did we get that? Subtract 3 from both sides and then divide by -2.

For a short review of the lesson, or if you are having difficulty, check out this lesson from Tarver Academy, called How to Solve Multi-Step Equations:

 

If you know how to solve a two-step equation and are having trouble, then all you have to do for a multi-step equation is think of each new line of the problem as a new two-step problem, and think to yourself, "How do I get that variable, x or gummy bear, by himself?

Let's give it a try in the Got It? section!

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