*Contributor: Elephango Editors. 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

subject

Math

learning style

Visual

personality style

Lion

Grade Level

Middle School (6-8), High School (9-12)

Lesson Type

Quick Query

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.

- 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?

You are probably familiar with solving one-step equations and using inverse operations:

x + 3 = 5

x + 3 - 3 = 5 - 3

x = 2

or

4x = 24

4x ÷ 4 = 24 ÷ 4

x = 6

- How did you solve these one-step equations?

You used inverse operations on both sides of the equal sign to isolate the x.

Once the x was isolated, you knew the value x was equal to.

Multi-step equations work the same way, but just have more steps!

The most important thing to remember about solving multi-step equations is to keep your work super organized so the steps do not confuse you.

First, let's look at what we know about this equation:

2x - 5 = 3

We know this is an *equation* because it has an equal sign. Expressions on both sides of the equal sign need to be equal.

The equation has a variable.

A *variable* is a symbol used in an equation to represent a value we do not know yet. In this case, the variable is an x.

- What else do you notice?

There are two *operations* in this equation.

There is subtraction represented by the minus symbol (-). There is also multiplication because the x has a coefficient of 2.

A *coefficient* is a number that the variable is multiplied by.

Now, that we have some information, we are ready to begin solving the equation for x.

To keep ourselves organized, draw a straight line down from the equal sign. This reminds us to keep both sides of the equations balanced or equal:

Remember our goal is to isolate the x, or get the x by itself. The first step we should take is to get rid of any numbers not connected to the x.

Notice the 5. It is not connected to the x. We should get rid of that number first.

Look at the sign in front of the x. To get rid of the 5, we need to use the inverse operation.

- What inverse operation should we use?

We will add 5 to each side of the equation.

Now, the equation will read:

2x = 8

The next step is to get rid of the coefficient of 2.

- What inverse operation should we use?

When solving equations, the symbol we will use for division is the fraction bar. We will divide both sides of the equation by 2:

Now, we know what x will equal!

You just solved your first multi-step equation!

Let's try one more before we move on. You will need a piece of paper and a pencil.

This time, let's use fractions in our equations!

1 | y | + | 9 | = | 14 | |

3 |

- What do you notice about this equation?
- What is the variable?
- What operations do you see?
- What inverse operations will you use?

This equation has a fraction, which seems scary! However, if you look closely it is pretty simple.

Think of y and the coefficient of ^{1}/_{3} like this:

1 | x | y | = | y | |

3 | 1 | 3 |

Now, rewrite the original equation.

y | + | 9 | = | 14 | |

3 |

- Does it look easier to solve now?

Same steps as before. First, draw a line down from the equal sign:

- Do you think you can solve the rest of this equation?

Remember to first get rid of any numbers not connected to y. Use inverse operations.

Then, get rid of the 3 under the fraction bar. Remember that the fraction bar is also a symbol for division!

- Have you completed all the steps and solved the equation?

- Does your paper look similar to the image above?

Fix any mistakes you made.

Next, move on to the *Got It?* section to practice more multi-step equations.