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**My Math Project**

By:

P.S.

That's Me

Bella Caruso

8

th

**Solving 2 Step Equations**

**Vocabulary**

Words

Words

Like Terms

- are #s and separate variables. Also, #s and variables together are one whole term.

Ex: 2, n, and 2n

Reciprocal

- is a number that you multiply by so that the result equals 1.

Ex: 2n

Inverse Operation

- is a function that undoes another function

Ex: 2

Equation Example:

3n + 7 = 19

There is 1 thing

we need to go over

before we start solving...

Distributive Property

Now...

...the fun...

... Begins!

- when you multiply the # outside of the ( )s.

Ex: 2(3 x 5n) 6 x 10n

5n +2(11 - n) = -5

The first thing you should always do is keep change flip. This means to change the - to a + and make the number behind it a -#. So,...

5n +2(11 - n) = -5

5n +2(11 + -n) = -5

Now, we start to solve by doing the...

...Distributive Property.

You multiply the # outside of the ( )s to each of the #s inside of the ( )s.

5n +2(11 + -n) = -5

5n + 22 + -2n = -5

5n +2(11 + -n) = -5

Now that we did the distributive property, now we will combined like terms.

5n + 22 + -2n = -5

+

Like terms are the #s and separate variables. Also, #s and variables together are one whole term.

5n and -2n are like terms. So, we will combined them.

3n +22 = -5

5n +2(11 + -n) = -5

5n +22 + -2n = -5

3n + 22 = -5

The next step is to get rid of the term without a # and a variable.

In this case we are trying to get rid of

22.

Remember:

What ever you do to one side, you must do to the other!

3n + 22 - 22 = -5 - 22

3n = -27

3n = -27

Now our last step is to isolate the variable. (

n

)

Remember:

What ever you do to one side, you must do to the other!

If the # is being multiplied by the variable then, you divide. the same thing goes for the other way around.

3/3n = -27/3

n = -9

Now that you know how to do 2 Step Equations, we can now move on to a Multi-Step Equations.

Equation Example:

-------------------------------------

5n +2(11 - n) = -5

3n + 7 = 19

The first thing we need to do is get rid of the constant. (

7

)

Remember:

What ever you do to one side, you must do to the other!

3n + 7 -7 = 19 -7

3n = 12

Now our goal is to isolate the variable.

3n = 12

Remember:

What ever you do to one side, you must do to the other!

3/3n = 12/3

**n = 4**

Now that you hav learned to do a 2 Step Equations and a Multi-Step Equations, we can learn the final type of equation.

Equations With Variables On Both Sides.

---------------------------------------------------------------

Equation Example:

7 - 8n = 4n -17.

7 - 8n = 4n - 17

These types of equations are different. First we are going to take away the smallest term.

( a # with a variable -

4n

)

7 - 8n - 4n = 4n - 4n - 17

7 - 4n = 17

7 - 4n = 17

Now it looks like a 2 step equation.

Do you remember what comes next?...

We get rid of the constant.

7 +7 - 4n = 17 + 7

4n = 24

4n = 24

Now we are going to isolate the variable.

4/4n = 24/4

**n = 6**

x

x

o