Algebra

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Algebra

• CRCT review

Ms. Jennifer Heins
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Variable

• A letter that is used to represent a number

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Algebraic expression

• An expression that includes one or more variables
• k
• 3x - 16

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equation

• a mathematical sentence that contains an equal
  sign
• 3x 11
• d 9 17
• -2z 5 15
• y 4 3y - 7

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coefficient

• The number being multiplied by the variable
• 5x
• 3y - 14x

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Order of Operations

• Brackets
• Parentheses ( )
• Exponents
• Multiplication/Division from left to right
• Addition/Subtraction from left to right

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Order of Operations Example 1
27 6(-2)
27 12
2 (-5)
-10
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Order of Operations Example 2
-6 3 12
-18 12
-6
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Writing Algebraic Expression

• NO EQUAL SIGN in an expression
• The quotient of seven and a number
• Ten less than one-third of a number

7
x
or
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Writing Algebraic Expression (cont.)

• A taxi charges a flat rate of 2 plus 2.50 per
  mile driven. Write an algebraic expression for
  the total cost of a taxi ride that went m miles.

m
2
2.5
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Writing Algebraic Expression (cont.)

• Amy brought some cookies to school. She gave 5 to
  her teacher and then divided the rest equally
  among the 24 students in her class. Write an
  algebraic expression for the number of cookies
  each student received.

c
-
5
24
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Commutative Property

• The sum of two numbers is the same no matter
  which order is used to add/multiply them.
• of addition a b b a
• of multiplication cd dc

HINT People commute move back and forth from
work daily
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Associative Property

• The sum/product of three numbers is the same
  whether you group the first two numbers or the
  second two numbers
• of addition (a b) c a (b c)
• of multiplication (de)f d(ef)

HINT Think about groups at school, or teams
who you associate with
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Identity Property

• of addition The sum of any number and 0 is that
  number
• 7 0 7 x 0 x
• of multiplication The product of any number and
  1 is that number
• 8 1 8 1y y

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Additive Inverse Property

• The sum of a number and its opposite is zero
• 5 (-5) 0
• (-x) x 0

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Combining Like Terms

• Must have the same variable and the same exponent

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Combining Like Terms Example 1

• Simplify.
• 7 5x 2 8x

-3x
9
-3x and 9 are NOT like terms, so they cant be
combined. This is written in simplest form.
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Combining Like Terms Example 2

• Simplify.
• 8m 2n 3 m 5n 7

7m
- 3n
- 4
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Combining Like Terms Example 3

• Simplify.
• 4x² - 7x 15 8x 10

4x²
x
5
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Distributive Property

• To multiply a number by a sum/difference of two
  terms, you can multiply that number by each term
  and add/subtract the two products.
• a(b c) ab ac
• d(e f) de - df

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Distributive Property Example 1

• Simplify.
• 8(2g - 5)

16g
- 40
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Distributive Property Example 2

• Simplify.
• -6(-y 4)

- 24
6y
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Distributive Property Example 3

• Simplify.
• -(-4 - 2b)

4
2b
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Distributive Property Example 4

• Simplify.
• 10 - (6x 7)

10
- 6x
- 7
- 6x
3
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Distributive Property Example 5

• Simplify.
• -(a 3) - 2(5 - a)

-a
- 3
- 10
2a
a
- 13
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Solving 1 step equations

• Addition Subtraction are inverse operations
• Multiplication Division are inverse operations
• What you do to one side of an equation, must be
  done to the other side of the equation

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Solving 1 step equations Ex 1

• Solve.
• -8 y -15
• 8 8
• y -7

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Solving 1 step equations Ex 2

• Solve.
• -100 -4u
• -4 -4
• 25 u

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Solving 1 step equations Ex 3

• Solve.

4
4
c -80
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Solving 1 step equations Ex 4

• Solve.
• q 6 -2
• - 6 - 6
• q -8

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Solving 2 step equations

• Undo addition or subtraction first
• Undo multiplication/division second

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Solving 2 step equations EX 1

• Solve.
• -3y 7 2
• 7 7
• -3y 9

-3 -3
y -3
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Solving 2 step equations EX 2

• Solve.

7 7
2
2
f 12
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Solving multi step equations

• 1. Distributive Property (if applicable)
• 2. Combine Like Terms (if applicable)
• 3. Cancel out fractions (if applicable)
• 4. Undo addition/subtraction
• 5. Undo multiplication/division

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Solving multi step equations EX 1

• Solve.
• -8a 15 4a 9

-12a
- 15
9
15
15
-12a 24
-12
-12
a -2
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Solving multi step equations EX 2

• Solve.
• 4(2c 3) 7 13

8c
12

- 7 13
8c
5
13
- 5
- 5
8c 8
8
8
c 1
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Solving multi step equations EX 3

• Solve.

2
2
3x 9 18
9 9
3x 27
3
3
x 9
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Relations Functions

• Relation any set of ordered pairs
• x-values are called inputs (domain)
• y-values are called outputs (range)
• function
• a relation where each input has only 1 output
• passes the vertical line test

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Functions (cont.)
This is a function, because it passes the
vertical line test.
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Functions (cont.)
This is a not a function. It doesnt pass the
vertical line test.
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Functions (cont.)

• State whether the data listed is a function.
• (0,2), (1,1), (2,2), (4, 3)
• Is a function, none of the x-values repeat
• (1,1), (3, -2), (4, 16), (1, -5)
• Not a function the x-value of 1 is paired with
  two different y-values 1 and -5
• (1,2), (2, 3), (-1, -2), (-2, -3)
• Is a function, none of the x-values repeat

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Functions (cont.)

• (-1, 2), (2, 5), (4, 9), (6, 11)
• What is the domain of the above function?
• -1, 2, 4, 6 (all of the x values)
• What is the range of the above function?
• 2, 5, 9, 11 (all of the y values)

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Direct Variation

• As x increases, y increases
• In a table, y divided by x is constant

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Inverse Variation

• As x increases, y decreases
• In a table, x times y is constant