untitled

Algebra

​

Multiple Choice

Simplify the expression 2x + 4x

• 5x

• 10x

• 6x

• x

Multiple Choice

Simplify 5x + 4y +2x + 8y

• 7x+12y

• 19xy

• 10x+32y

• x+y

Multiple Choice

Simplify the expression 5x + 3y

• 7xy

• 5xy

• 5x+3y

• 15 xy

Multiple Choice

Simplify 3x + 4y + 6x + 4y

• 6x +4y

• 9x+ 8y

• 7xy + 10xy

• 17xy

Multiple Choice

Simplify 6 $x^2$  -7x-3 $x^2$ + 4x 

• 9 $x^2$  + 11x

• 3 $x^2$  - 3x

• 3 $x^2$  - 10x

• 9 $x^2$  

Multiple Choice

Simplify 8m+9n-3m-5n

• 11m +4n

• 5m+14n

• 11m+14n

• 5m +4n

Multiple Choice

Simplify -3x+ 4y +8x - 2y

• 11x+6y

• -5x+2y

• 5x +2y

• x+y

Poll

You are given part of a sum and the answer.

Can you complete the rest of the sum?

3x + 2y + …x + …y = 8x + 4y

• 5x,2y

• 2y,5x

Poll

You are given part of a sum and the answer.

Can you complete the rest of the sum?

4x – 3y + …x + …y = 2x + 4y

• 2x, 7y

• -2x , 7y

Multiple Choice

a)x terms are the same as 

 $x^2$  terms

• True

• False

Multiple Choice

a)xy terms are the same as yx terms.

• True

• False

Poll

I can collect like terms in linear expressions.

Poll

I can simplify algebraic expressions by collecting like terms.

ALGEBRA

Teachers:

Mr. Bowie

Ms. Lawrence

Translate Word Phrases to Algebraic Equations

Remember, an equation has an equal sign between two algebraic expressions. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean equals.

Some words that translate to the equal sign are:

• is equal to

• is the same as

• is

• gives

• was

• will be

Translate the sentence into an algebraic equation: The product of 8 and 7 is 56.

• Locate the “equals” word(s). is

• Write the = sign.

• Translate the words to the left of the equals word into an algebraic expression. 8 x 7 = _

• Translate the words to the right of the equals word into an algebraic expression. 8 x 7 = 56

Example

A number n times 3 is equal to 120.

This is an easy one. The word "times" tells you that you must multiply the variable n by 3, and that the result is equal to 120. Here's how to write this equation:

3n = 120

Tim worked for 7 hours on Saturday and mowed 3 lawns. How much time, on average, did he spend on each lawn?

Let the letter "t" represent the average time per lawn, the unknown value. Then, 3t would represent the time to mow all three lawns, and we know that this is equal to 7 hours. We can write the equation like this:

3t = 7 hours

Translate the sentence into an algebraic equation

• The sum of 6 and 9 is 15

  6 + 9 = 15

• The sum of 3 and 4 gives 7

• 3 + 4 = 7

  Three more than x is equal to 47

  x + 3 = 47

• six less than x is equal to 35

  x - 6 = 35

Multiple Choice

Translate “a number decreased by eight equals twelve” into an equation

• $\frac{8}{x}\ =\ 12$

• x + 12 = 8

• x - 8 = 12

• $\frac{x}{8}\ =\ 12$

Multiple Choice

You are planning a party for all of your friends. The cost of renting a room is $35, cost of food per person is $4.

How much will it cost if I brought 8 people to the party?

• $67

• $57

• $70

• $83

Multiple Choice

Five times a number is equivalent to thirty-two less than nine time the same number.

• 5x - 32 = 9x

• 5x = 9x - 32

• 5x = 9x + 32

• 5x - 9x = 32

Multiple Choice

Twice the difference of a number and 16 is equivalent to 28.

• 2x + 16 = 28

• 2x - 16 = 28

• 2(x + 16) = 28

• 2(x - 16) = 28

Multiple Choice

One - third of the sum of a number and 24 is equivalent to 10.

• 1⁄3(x + 24) = 10

• 1⁄3x + 24 = 10

• 1⁄3(x - 24) = 10

• 1⁄3x + 10 = 24

Multiple Choice

Three times the sum of a number and 7 is equivalent to 57.

• 3x + 7 = 57

• 3(x + 7) = 57

• 7x + 3 = 57

• 7(x + 3) = 57

Multiple Choice

A gymnastics center charges a $60 registration fee and $15 per class. Olivia registers to take a class and pays a total of $210. Which equation can be used to determine how many classes Olivia signed up for?

• 60 - 15x = 210

• 15x - 60 = 210

• 15x + 60 = 210

• 210 + 15x = 60

Multiple Choice

Justin is purchasing a new iPhone. The sales clerk says that if he pays $100 now his monthly payments will be $25 and his total cost will be $600. Which equation can be used to determine how many months Justin will be paying for his phone?

• 25x + 100 = 600

• 25x - 100 = 600

• 600 - 100x = 25

• 600 + 25x = 100

Algebra Review

Let's See What You Remember!

Equations

Isolate the variable by using inverse operations.

Isolate = by itself

Variable = letter representing an unknown number

Inverse Operations = opposite (add/subtract or multiply/divide)

One Step Equations

Undo the operation to solve for your variable.

Multiple Choice

Solve for b.

9b=18

• 9

• 2

• 27

• -11

Multiple Choice

Solve for x.

x + 17 = 4

• 21

• -13

• 68

• $\frac{4}{17}$

Two Step Equations

Undo the operations while following reverse of PEMDAS.

Multiple Choice

Solve for n.

-6n + 6 = 60

• -20

• 18

• -9

• -16

Multiple Choice

Solve for x.

 $\frac{x}{5}-10=-10$  

• 0

• 18

• -25

• 1

Multiple Choice

Solve for r.

 $-6r-9=111$  

• -6

• -17

• 11

• -20

Multiple Choice

Solve for x.

 $8\left(1+x\right)=-8$  

• 10

• 7

• -2

• 17

Multi-Step Equations with Variables on One Side

1. Distribute (if needed)

2. Combine like terms (if needed)

3. Solve the remaining equation.

Multiple Choice

Solve for a.

-a + a = 0

• Infinite Solutions

• No Solution

• 0

• 1

Multiple Choice

Solve for x.

 $3\left(1+7x\right)-7=-88$  

• -12

• -4

• 16

• Infinite Solutions

Multi-Step Equations with Variables on Both Sides

1. Distribute (if necessary)

2. Combine Like Terms on the same side (if necessary)

3. Use opposite operations to get like terms together across the equal sign.

4. Solve!

Multiple Choice

Solve for n.

 $n+14\ =\ 5n-2$  

• 4

• 0

• 2

• -1

Multiple Choice

Solve for r.

 $-26+4r=-2\left(3-4r\right)$  

• 7

• -4

• 11

• -5

Proportions

1. Cross Multiply

2. Distribute (if necessary)

3. Combine like terms (if necessary)

4. Solve!

Multiple Choice

Solve the proportion for x.

 $\frac{10}{5}=\frac{x}{2}$  

• 4

• 7.494

• 2

• 2.3

Multiple Choice

Solve the proportion for x.

 $\frac{9}{8}=\frac{10}{\left(x-3\right)}$  

• 11.89

• 1

• 7.05

• -2.5

Poll

How did you feel you did?

• AWESOME

• PRETTY GOOD

• OKAY

• BAD

• TERRIBLE

Evaluating Functions

Algebra

Goals:

• Determine output values given input values

• Determine input values given output values

Key Words

• Evaluate: to determine the value of something

• Function: a relation in which each element of the domain is mapped to (paired with) exactly one element of the range

• Input: the value that is transformed by a process and becomes an output

• Output: The result of an input that has been transformed by a process

Multiple Choice

 $f\left(2\right)=?$  

• -2

• -6

• -38

• 58

Finding an output value

Multiple Choice

 $f\left(1.5\right)=?$  

• 0

• 2

• 6

• -1

Determine the input of a function

Multiple Choice

 $f\left(x\right)=\frac{1}{4}x+3$  Determine the input value that would give an output value of  $\frac{14}{4}$  .

• 0

• 1

• 2

• 3

Poll

Rate your level of understanding

• 5- I've got this

• 4 - I am getting the hang of it

• 3 - Practice will help me fully understand

• 2- I have some questions

• 1 - I am lost

Multiple Choice

 $f\left(x\right)=\frac{1}{3}x+2$  

What is the inverse of the equation above?

•  $h\left(x\right)=\frac{1}{3}x-2$  

•  $h\left(x\right)=\frac{1}{3}x+2$  

•  $h\left(x\right)=3x-2$  

•  $h\left(x\right)=3x-6$  

Direct and Indirect Variation

Algebra 1

Mrs. LaGrange

Direct Variation

Since y depends on x, y is the dependent variable and x is the dependent variable. Notice that as x increases y also increases.

Direct variation equations are of the form y = kx where k does not equal 0.

k is called the constant of variation (sometimes constant of proportionality).

Finding the Constant of Variation:

If we are given y and x we can find k.

k =y/x

Multiple Choice

In a direct variation, y = 39 when x = 3. 
Find the value of y when x = 2.

• 26
• 3
• 58.5
• 2

Multiple Choice

Is this a direct variation?

• yes
• no

Multiple Choice

Write the equation for the table given.

• y = 1/3x
• y = 3x
• y = 1/2x

Multiple Choice

Is this a direct variation?
y = 2x

• yes
• no

Multiple Choice

Is the given table a direct variation? If so, what is the constant?

• Yes; 1/4

• Yes; 4

• Yes; 2

• No

Inverse Variation (sometimes called Indirect Variation)

We say that y varies inversely with x. In other words as x increases, y decreases.

y=k/x or xy = k

Finding the Constant of Variation.

To find the constant of variation k, for inverse variation, multiply x and y.

k=xy

Multiple Choice

x and y vary inversely. Given (5, 20), what is the constant k?

• 4
• 5
• 25
• 100

Multiple Choice

• direct variation
• inverse variation
• neither direct nor inverse variation

Multiple Choice

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k? 

• 121
• 4
• 100
• 6

Multiple Choice

Is the given table a direct or inverse variation? What is the constant of variation?

• Direct, 12
• Inverse, 12
• Direct, 1/12
• Inverse, 1/12

Summary:

Direct Variation: As x increases, y also increases.

Inverse (Indirect) Variation: As x increases, y decreases.

Multiple Choice

Is the given table a direct variation? If so, what is the constant of variation?

• Yes; 1/3
• Yes; 3
• Yes; 5
• No

Multiple Choice

The equation 
xy =  25  represents:

• direct variation
• inverse variation
• joint variation
• none of these

Multiple Choice

• direct variation
• inverse variation
• neither direct nor inverse variation

Multiple Choice

Is this a direct variation?

• yes
• no

Multiple Choice

Is this a direct variation?

• yes
• no