Quarter 3 Review Pre-Algebra

Distributive Property

For the problem 9(4+3)...

• The 9 is outside the parenthesis so this is the number that needs to be multiplied by EVERYTHING inside the parenethesis

Multiple Choice

Use your notes to write this equation in another form...

2(5+3)

• 15+10

• 10+6

• 6+15

Using Variables

• Multiply 5 times x

• Multiply 5 times 6

• We multiply the outside number by all terms on the inside of the parentheses.

Multiple Choice

Which is equivalent to 5(a + 6)?

• 5a + 6

• a + 30

• 5a + 30

• 5a - 30

Multiple Choice

2(4k + 7)

• 4k-9

• 4K+9

• 8k-14

• 8k+14

Multiple Choice

Simplify 5(2 - 7n)

• 52 - 57n

• 10 - 7n

• 10 - 35n

• 10 + 35n

Match

Match the following each expression with what it would be AFTER you distribute.

• 6(x - 3)

• 6(x + 3)

• -6(x - 3)

• -6(x + 3)

6x - 18

6x + 18

-6x + 18

-6x - 18

• 6x - 18

• 6x + 18

• -6x + 18

• -6x - 18

When you combine like terms...

• You can only add things that are alike. Example- 2x & 7x

• You need to use the sign in front of the number to determine if the number is a positive or a negative.

Combing Like Terms

• You have to combine like terms

• x with x and y with y and numbers with numbers

• Remember your signs

Cobine like terms

• If you have 4x+5x

• Just add 4+5

• equals 9

• Then add x to the end

• The final answer is 9x

Multiple Choice

Which expression is the simplified form of 6x + 5x

• none of these

• 11

• 11x

• 12x

Cobine like terms

• If you have multiple terms then look to see what is the same for each term

• Example: 3 + 6x + 8 + 2x

• First combine "x's" so 6x + 2x = 8x

• Then combine what is leftover 3+8 = 11

• Now put the two answers together

• 8x+11

Multiple Choice

Simplify: 3x + 5 + 2 + 9x

• None of these

• 8x + 11

• 3x + 7

• 12x + 7

Remember your signs

• -2x + 9x is not 11x

• since 2 is negative think of subtracting

• 9 - 2 is 7 so -2x + 9x = 7x

Multiple Choice

What is the value of 6x + 3 - 8x - 5?

• -2x - 2

• 2x + 2

• 2x - 2

• -2x + 2

What is the value of 6x + 3 - 8x - 5?

• First combine 6x and -8x

• Since 6 - 8 = -2 then it is -2x

• Then combine 3 and -5

• 3 - 5 = -2 also

• Put the two answers together to get -2x - 2

Multiple Choice

What is 5m + 7 - 2m + 4m - 15

• 9m + 7

• 7m - 8

• 9m - 8

• 7m - 15

What is 5m + 7 - 2m + 4m - 15

• Start with 5m - 2m = 3m then add the last m value of 4

• So 3m + 4m = 7m

• Then look what is left to combine 7 and -15 again since negative think subtract

• So 15 - 7 = 8 and take the sign of the bigger number so since 15 is negative and it bigger than 7 the final answer is -8

• Put it all together and your final answer is 7m - 8

Multiple Choice

What is -x + 4x - 6x - 8x

• -11

• -11x

• 12x

• -12x

Multiple Choice

$$2x^2+4x-5x^2+6$$ Simplify. Venture into the dark woods.

• $$x+6$$  

• $$x^2+6$$  

• $$-3x^2+4x\ +6$$  

• $$3x^2+4x+6$$  

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​Solving Multi-Step Equations

Follow along and answer the question in this Quizizz Lesson.

In case you need a little help, I have included some informational slides to help out.

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Simplifying before Solving

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As you can see in the photo to the right, some equations must be simplified before they can be solved.​

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The goal is to simplify the equation into a two-step equation.​

​The first 3 steps of this problem show how to simplify the equation.

After simplifying, we can see that ​we have a two-step equation and we use inverse operations to solve.

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If an equation contains parentheses, like the ones you see in these examples, you must distribute the value on the outside to get rid of the parentheses.

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Remember, distribute means to multiply!​

Distributive Property

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​With all POSITIVE values.

​Be careful with negatives!

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

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

Combine ALL like terms.

$$3\ +\ 4m\ +5\ +\ m\ =\ 23$$  

• 3 + 4m + 5 = 23

• 5m + 8 = 23

• 4m + 8 = 23

• 3 + 5m + 8 = 23

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.​

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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:

$$2x-3+5x=18$$  

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

Multiple Choice

Simplify the following equation and solve for x:

$$2x-3+4x=27$$  

Show your work on page 24 of your notebook.

• x = 12

• x = 4

• x = 5

• x = 15

Multiple Choice

Simplify the equation and solve for the variable.

$$24\ =\ 3\left(3x\ -7\right)$$

Show your work on page 24 of your notebook.

• $$x\ =\ -9$$  

• $$x\ =\ 5$$  

• $$x\ =3$$  

• $$x\ =\ 7$$  

Multiple Choice

Simplify the following equation and solve for x:

$$3x+2(4x-4)=3$$  

Show your work on page 24 of your notebook.

• x = 4

• x = 3

• x = 2

• x = 1

Multiple Choice

Solve for v.

• 60

• -3

• 15

• 3

Multiple Choice

$$96=6\left(k+8\right)$$  

• $$12$$  

• $$8$$  

• $$-4$$  

• $$9$$  

La x positiva también se puede representar con un rectángulo amarillo

Multiple Choice

Which set of algebra tiles represents the equation x+2=10?

Multiple Choice

Which equation does this set of algebra tiles represent?

• x+8=14

• x+9=14

• x+9=22

• x+8=22

Multiple Choice

Which model represents this equation?

Multiple Choice

Which model represents X + 6 = 2 ?