CW: Equations Lesson

8.17 Solving Multi-Step Equations

Some text here about the topic of discussion

Reorder

Place the following in the correct order of how to solve an equation:

• Distributive Property

• Combing Like Terms

• Variables on One Side

• SADMEG

1

2

3

4

• 1
• 2
• 3
• 4

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 Choice

Terms that have the same variables such as 5x and -8x.

• like terms

• coefficients

• exponents

• variables

Multiple Select

Check all the boxes that show like terms.

• 5x and x

• -3 and 2

• 8 and x

• 7y and 9y

• 8x and 5

Multiple Choice

Combine ALL like terms.

$$3\ +\ 4m\ +5\ +\ m\ =\ 23$$  

• 3 + 4m + 5 = 23

• 5m + 8 = 23

• 4m + 8 = 23

• 3 + 5m + 8 = 23

Multiple Choice

Le's practice combining like terms.

Simplify: 7x - 8 + 3x - 1

• 10x - 9

• 21x + 8

• 4x + 9

• 10x + 9

Multiple Choice

Simplify the expression:

3x + 6 + 7x

• 10x + 6

• 21x + 6

• 16x

• 9x + 7

​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.

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.​

​

Let's Solve: -8(-8x - 6) = -8x - 22 + 2x

Step One: Distribute

Multiple Choice

After applying the distributive property to the following equation, what would be the result: -8(-8x - 6) = -8x - 22 + 2x

• 64x + 48 = -8x - 22 + 2x

• -64x - 48 = -8x - 22 + 2x

• 8x - 6 = -8x - 22 + 2x

-8(-8x - 6) = -8x - 22 + 2x

64x + 48 = -8x - 22 + 2x

Step Two: Combine Like Terms

Multiple Choice

After combining like terms in the following equation, what would be the result: 64x + 48 = -8x - 22 + 2x

• 64x + 48 = -10x -22

• 112 = -28x

• 64x + 48 = -6x - 22

-8(-8x - 6) = -8x - 22 + 2x

64x + 48 = -8x - 22 + 2x

64x + 48 = -6x - 22

Step Three: Move your variable to one side of the equation.

Multiple Choice

After moving the variable to one side in the following equation, what would be the result: 64x + 48 = -6x - 22

• 70x + 48 = -22

• 58x + 48 = -22

• 48 = 70x - 22

-8(-8x - 6) = -8x - 22 + 2x

64x + 48 = -8x - 22 + 2x

64x + 48 = -6x - 22

70x + 48 = -22

Fourth Step: Move your constant to one side of the equation.

Multiple Choice

After moving the constant to one side in the following equation, what would be the result: 70x + 48 = -22

• 70x = 70

• 70x = -70

• 70x + 70 = 0

-8(-8x - 6) = -8x - 22 + 2x

64x + 48 = -8x - 22 + 2x

64x + 48 = -6x - 22

70x + 48 = -22

70x = -70

Final Step: Solve by isolating the variable (multiply or divide)

Multiple Choice

What is the solution to the equation: 70x = -70

• 1

• 70

• -1

• -70

Multiple Choice

What is the first step in solving the equation:

$$4\left(x-2\right)=12$$  

Multiple Choice

What is the first step in solving the equation:

$$4x-8=12$$  

Multiple Choice

What is the first step in solving the equation:

$$2x-3+5x=18$$  

Multiple Select

What is the first step in solving the equation:

$$2x-3=5x+9$$  

Multiple Choice

How do you "move" 3 to the other side of the equal sign?

$$4x+3=7$$  

• add 3

• subtract 3

Multiple Choice

How do you "move" 5x to the other side of the equal sign?

$$2x+11=5x-10$$  

• subtract 5x

• add 5x

Multiple Choice

How do you "move" -7x to the other side of the equal sign?

$$-7x-9=15+17x$$  

• subtract 7x

• add 7x

Multiple Choice

What is the coefficient of x?

$$-3x\ =\ 12$$  

• -3

• 12

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

Fill in the Blank

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

$$3\left(t\ +3\right)\ +\ 7\ =\ 49$$  

Fill in the Blank

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

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

Fill in the Blank

$$6x\ +\ 5x\ -\ 8\ +\ 2\ =\ 5$$  

Solve for x.

Multiple Choice

-(n - 8) = -2

• 6

• 10

• -10

• -6

Fill in the Blank

Solve the following equation. (Type in the number only)

$$-9=p-4p$$  

Fill in the Blank

Solve the following equation. (Type in the number only)

  $$-5(4x+4)=140$$  

Fill in the Blank

Solve the following equation. (Type in the number only)

  $$95=6(p+3)+5p$$   

Fill in the Blank

Solve the following equation. (Type in the number only)

  $$23=-3(2p+7)-(7p+8)$$    

Fill in the Blank

Solve the following equation. (Type in the number only)

  $$-6(a+3)-8(2-2a)=36$$    

Fill in the Blank

Solve the following equation. (Type in the number only)

  $$-312=8(-6v+3)$$     

Fill in the Blank

Solve the following equation. (Type in the number only)

  $$x-2x=-2$$      

Multiple Choice

3x + 2(4x - 4) = 3

• 4
• 3
• 2
• 1

Multiple Choice

-(n - 8) = -2

• 6
• 10
• -10
• -6

Multiple Choice

Solve

-19 = -8 (-4+a) - (2a+1)

• -1

• 14

• -5

• 5

Multiple Choice

Solve

-124 = 4 (1+ 8k)

• -11

• 10

• -4

• -2

Multiple Choice

8v - 4(v + 8) = 8

• 2
• 10
• 4
• -4