Multi-Step Equations (Sept 13th)

An Equation is a statement that says both sides of the equal sign are equivalent, or the same.

Here are the steps to solving a multi-step equation:

• Distributive Property

• Combine like terms (​on the same side of the equation)

• Use inverse operations ​to put variables and constants on opposite sides of the equations

• Isolate the variable​

Subject | Subject

Multiple Choice

What is the first thing you should do to simplify an equation?

• add

• Distributive Property

• Combine like terms

• divide

​How can you tell that you need to use the Distributive Property?

You will see a term sitting next to parentheses, ready to be multiplied to the terms inside the parentheses. Like these:

• ​4(x - 7) = -9

• -8x + 3 = 2 - 8(x + 4)​

Multiple Select

Which of the following equations require you to use the Distributive Property first? Select all that apply.

• 6x - 8 = 7(x + 2)

• 7n - 5 = 3

• 2(a - 9) = 9a + 1

• 4 - 9y+ 8 +2y

Multiple Choice

Let's practice using the Distributive Property.

Simplify: 6(x - 3)

• x - 18

• 6x + 18

• 6x - 9

• 6x - 18

Multiple Choice

Simplify: -3(n - 8)

• 3n - 8

• -3n - 24

• -3n + 24

• -24

Once you distribute, check to see if you have like terms, on the same side of the equal sign. Here are some examples of like terms:

• 5x and -6x

• -6 and 3 *** Remember that constants (regular numbers) are like terms with each other. ***

• 7m and m ​

Multiple Select

Check all the boxes that show like terms.

• 5x and x

• -3 and 2

• 8 and x

• 7y and 9y

• 8x and

Multiple Choice

Le's practice combining like terms.

Simplify: 7x - 8 + 3x - 1

• 10x - 9

• 21x + 8

• 4x + 9

• 10x + 9

​Once you distribute and combine like terms, make sure variables are on one side and constants (regular numbers) are on the other side. Use inverse operations to move terms to the other side.

Multiple Choice

If we wanted to get the variable by itself, what is this first operations we would use to accomplish this?

7x - 8 = 27

• Add 8 to both sides

• Subtract 8 on both sides

• Subtract 27 on both sides

• Divide by 7 on both sides

Multiple Choice

After adding 8 to both sides, we would get:

7x = 35

What is our next step

• Subtract 35 on both sides

• Multiply by 7 on both sides

• Divide by 7 on both sides

Here is an example of how to solve a multi-step equation. See if you can follow the steps that are written on the side.​

​

Multiple Choice

Find the solution to the following equation:

-5n + 6n + 15 - 3n = -3

(This is #7 on page 4 in your packet)

• n = 9

• n = -9

• n = -18

• n = 18