8th Grade Unit 1: Remediation & Re-Take

Unit 1 Assessment:
Remediation &
Re-Take

Solving one-step equations

• Use an inverse operation to get to the variable by itself

• Check your answer

Multiple Select

Check all that apply:

2.5 + A = 23.4

• the inverse operation of addition is subtraction

• + 2.5 on both sides

• -2.5 on both sides

• A = 21.1

• Check your answer by replacing the variable with its value

Solve two-step equations

• What are you solving for?

• + or - to isolate the variable term.

• × or ÷ to solve for the variable.

Multiple Select

Check all that apply:

5v + 4 = -26

• First step: +26 on both sides

• First step: -4 on both sides

• Second step: +26 on both sides

• Second step: -5 on both sides

• Second step: divide by 5 on both sides

Fill in the Blank

What is the value of v?

5v + 4 = -26

v = ?

Type the number, no space.

-

Solving multi-step equations

• Can you distribute?

• Can you combine like-terms?

• Use inverse operations to solve.

Multiple Select

Check all that apply:

-28 = 2a + 8 - 5a

• I can use distribution

• I can combine like-terms

• -28 and +8 can be combined

• 2a and -5a can be combined

• -28 = -3a + 8

Fill in the Blank

What is the first step in the equation?

-2 (x - 4) = 10

Variables on both sides

Move all variable terms to one side

Multiple Choice

How to move all variables to one side?

2x - 4 = x + 5

• +4 on both sides

• -5 on both sides

• +2x on both sides

• -x on both sides

Multiple Select

How to move all variables to one side?

3a + 2 = 8a + 9

• -2 on both sides

• -9 on both sides

• -8a on both sides

• +8a on both sides

• -3a on both sides

Fill in the Blank

Solve for x.

4x - 6 = 2x + 2

Type the number, no space.

Can I combine like-terms here with the 3x and -x?

Hint: they have to be on the same side to combine.

Multiple Choice

Interpret the sentence:

Perimeter is twice the sum of length and width.

• p = 2 + l + w

• p = 2 x l + w

• p = 2 x (L + W)

Parts of an Algebraic Expression

Mrs. Shurer

Numbers, letters, and operators (+, -, x, /) grouped together to represent a value.

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An expression is a problem without an equal sign.​

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Expression

Multiple Choice

Which of the following is not an expression?

• 8a + (-9)

• -17 - 10

• 5x + 10 = -15

• 12 + (-5f)

Each piece (amount separated by an operator) of an expression is called a term.

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Terms

When determining if the term is positive or negative, use the sign in front of the term.

​

+ means the term is positive

​

​- means the term is negative

Terms

Multiple Choice

How many terms does the following expression have?

11x + 5 - 8x + 10 - x

• 4

• 5

• 3

• 2

Multiple Choice

How many terms are in the expression
3x + 2y + z

• 5
• 2
• 4
• 3

Expressions are made up of variable terms. Variable terms are terms with a variable in them.

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Parts of an eXPRESSion

​

​1

Multiple Choice

Identify the variable terms in the expression below:

7a - 14 + 8a + 9

• 7a, 8a

• 14, 9

• a

• -14, 9

Each variable term has a coefficient.

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The coefficient is the number attached to the variable by multiplication.​

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Parts of an eXPRESSion

​

1

Multiple Choice

Identify the variable terms in the expression below:

7x + 13 - 9x -15

• 7x, -9x

• 7x, 9x

• 13, -15

• x

Multiple Choice

Identify the coefficients in the expression below:

7a - 14 + 8a + 9

• 7a, 8a

• 7, 8

• a

• -14, 9

Numbers all by themselves, with no variables attached to them, are constants.

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"Constantly lonely"

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Parts of an eXPRESSion

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Multiple Choice

Identify the constants in the expression below:

7a - 14 + 8a + 9

• 7a, 8a

• 14, 9

• a

• -14, 9

Multiple Choice

Identify the constants in the expression below:

7x + 13 - 9x -15

• 7x, -9x

• 7x, 9x

• 13, -15

• 13, 15

• 7, -9

• Variable terms are terms with a variable.

• Coefficients are the numbers attached to the variables.​

• Constants are numbers all by themselves.​

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Parts of an

algebraic expression

Multiple Choice

Identify the variable in the expression 3x +  9

• x
• y
• 9
• 3x

Multiple Choice

How many terms are in the expression
3a + 2b + c + 100

• 3
• 4
• 5
• 6

Multiple Choice

The number before a variable is the _____.

• term
• constant
• coefficient
• variable

Multiple Choice

Find the coefficient in the algebraic expression.

• x
• 4
• 5
• 9

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One Solution, No Solution, All Solutions

One Solution, No Solutions, Infinite Solutions

One solution

• Means that only one number can make the statement true

• Solutions shown as: x=3, y=8, b=4, x = -5

• A way to tell if the equation only has one solutions is that there are a different amount of x's on each side

• For example: 4x = 6x or 5x+3= 8x+6

No solution

• Means that NO number you choose can make the statement true

• Solutions look like: 3=5 or -4 = 9 or 2 = -32

• A way to tell if the equation is NO solution is that there are the same amount of x's on each side but the constants are different on each side

• For Example: 3x +4 = 3x -5 or 6x - 4 = 6x + 10

Infinite (All) Solutions

• Means that no matter what number you give me it WILL be a solution to the equation

• Solutions look like: 2 = 2 or 4=4 or -3 = -3 or 0 = 0

• A way to tell if the equation is ALL solutions is that there are the SAME amount of x's on each side and there are the SAME amount of constants on each side.

• For example: 4x + 5 = 4x + 5 or 2x - 3 = 2x -3

Multiple Choice

What is the solution to this equation?

• One solution

• No solution

• Infinite (All) Solutions

• I am confused

Multiple Choice

What is the solution to the equations?

• One Solution

• No Solution

• Infinite Solutions

• I am confused

Multiple Select

What number do I need to be able to have All solutions? 3 = _

• 0

• - 3

• 6

• 3

Multiple Choice

How many solutions does this equation have?

6x + 9 = 3x + 9

• One Solution

• No Solution

• Infinite (All) Solutions

• I am confused

Multiple Select

What is the missing information that would make the statement true for NO solution?

3x + 5 = 3x + _

• 0

• -5

• 5

• 7

Multiple Select

What is the missing information that would make the statement true for One solution?

4x + 5 = _ - 6

• 4x

• 3x

• 10x

• 5x

Solving Inequalities

Same rules as solving equations

• Distribute

• CLT

• Get variables on the same side

• Add/subtract constants

• Multiply/divide coefficients​

When you multiply or divide both sides by a negative, you FLIP the inequality sign!

​Some text here about the topic of discussion.

​SPECIAL RULE

Multiple Choice

Decide if the following inequality will need to be flipped:

$$x-3<-16$$  

• Flip!

• Do not flip!

Multiple Choice

Decide if the inequality will need to be flipped:

$$-6x+5\ge35$$  

• Flip!

• Do not flip!

Multiple Choice

Decide if the following inequality will need to be flipped:

$$\frac{x}{2}+4>-7$$  

• Flip!

• Do not flip!

Closed Cirlce!

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Open Circle!​

​Graphing Inequalities

Some text here about the topic of discussion

Direction of the arrow

Multiple Choice

Open dot or closed dot?

$$g<-14$$  

• Open dot

• Closed dot

Multiple Choice

Open dot or closed dot?

$$y\ge5$$  

• Open dot

• Closed dot

Multiple Choice

Which way will the arrow on the number line point?

$$x<-6$$  

• Left

• Right

Multiple Choice

Which way will the arrow on the number line point?

$$h\ge8$$  

• Left

• Right

Multiple Choice

Which way will the arrow on the number line point?

$$-3<f$$  

• Left

• Right

Draw

Graph the inequality on the number line:

$$x<-4$$  

Multiple Choice

Solve the following inequality:

$$2x-5<13$$  

• x < 4

• x < 9

• x > 9

• x > 4

Multiple Choice

Solve the following inequality:

$$-3x-5\le22$$  

• $$x\le-9$$  

• $$x\ge-9$$  

• $$x\le\frac{-17}{3}$$  

• $$x\ge\frac{-17}{3}$$  

Multiple Choice

Solve for x. (Use the image to identify the correct inequality and graph.)

$$x\ -\ 1\ \le\ -9$$  

• A

• B

• C

• D

Multiple Choice

Solve for x. (Use the image to identify the correct inequality and graph.)

$$\frac{x}{8}\ >\ 4$$  

• A

• B

• C

• D