RE-LEARN SOLVING MULTI-STEP EQUATIONS

When solving multi-step equations:

• Distribute

• Combine Like Terms

• Add/Subtract to cancel the constant

• Multiply/Divide to isolate the variable

• Remember, you can always go back to the lesson to look at some more step by step examples if needed!

EXAMPLES with Distribution

4(n - 2) = 28

32 = -4(x - 3)

EXAMPLES with Like Terms

-8e + 7 + 3e = -13

1 - 3p − 5 = −16

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

$$7x-5x=6$$  

• 3

• 2

• -3

• 4

Multiple Choice

$$2x+2-8x=8$$  

• 0

• 1

• 3

• -1

Multiple Choice

$$42=2\left(1+4x\right)+2x$$  

• 10

• -1

• 11

• 4

Fill in the Blanks

Use the distributive property, combine like terms and simplify to find t.

$3\left(t\ +3\right)\ +\ 7\ =\ 49$  

Fill in the Blanks

Use the distributive property, combine like terms and simplify to find r.

$-5\left(3d\ +2\right)\ +\ 10=\ -15$  

Multiple Choice

$$42=2\left(1+4x\right)+2x$$  

• 10

• -1

• 11

• 4

Multiple Choice

Solve the following equation:

2m + 6m + 2m = 20

• m = 40

• m = 20

• m = 3

• m = 2

​STOP HERE UNTIL WE GET TO VARIABLES ON BOTH SIDES

Equations with variables on both sides

Notice there are variables on both sides

The goal is to have the variables on one side of the equation while having the constants (numbers) on the other

x = "constant"

To do that, we remove as many as we can from both sides

Fill in the Blanks

After removing the 3x from both sides, what will the equation look like?

DO NOT USE SPACES

Now we only have the variables on one side

We can move on to solving equations like you are used to

By removing the constants (on both sides) so that we have the variable (x) by itself

Multiple Choice

How many ones (yellow squares) can we remove from both sides?

• 2

• 4

• 6

• -2

We can subtract 2 from both sides

Fill in the Blanks

After subtracting 2 from both sides. How does the equation look like now?

DO NOT USE SPACES

​Solving Equations with Variables on Both Sides

• ​​Watch the video

• ​Record the examples and information on the notes page or in your notebook.

• ​Complete the "You Try" and check your work with Mrs. Jackson.

• ​Then, continue the rest of the lesson to get at least an 80%

Alternate method:

• Subtract 7x from both sides

- -13 = -10x - 33

• Add 33 to both sides

20 = -10x

• divide both sides by -10 and you still get x = -2

Multiple Choice

Which is the correct order in which to solve multi-step equations?

• Distribute

  Combine like terms

  Get the variable on one side by add or subtracting

  Divide or multiple

• Add or subtracting

  Distribute

  Combine like terms

  Divide or multiple

• Divide or multiple

  Add or subtracting

  Distribute

  Combine like terms

Fill in the Blanks

Solve: 2x - 5 = 4x + 3

Important: No spaces in your answer

Fill in the Blanks

3y - 8 = 7y

Fill in the Blanks

10x + 9 = 4x - 9

Fill in the Blanks

8x - 8 = -4x + 16

Fill in the Blanks

7w + 5 = 3w - 15