# 11-6 PPT

```5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
1. 4 (x + 2)
2. 5 (2x + 7)
3. 2( x + 4)
4. 6(5 + 2 x)
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
1. 4 (x + 2)
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
1. 4 (x + 2) = 4x + 8
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
2. 5 (2x + 7)
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
2. 5 (2x + 7) = 10x + 35
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
3. 2( x + 4)
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
3. 2( x + 4) = 2x + 8
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
4. 6(5 + 2 x)
5 Minute Check
Complete on the back of your homework. Use
the Distributive Property to rewrite each
algebraic expression.
4. 6(5 + 2 x) = 30 + 12x
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Work with a partner and complete page 494
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Thursday, Nov 6
Lesson 6.6.7
Equivalent Expressions
Equivalent Expressions
Objective: To understand how to use
properties to simplify expressions.
Equivalent Expressions
A term can be a single number or variable or
numbers and variables multiplied together
and separated by addition or subtraction.
e.g.
4x + 4
This expression has 2 terms.
Equivalent Expressions
A coefficient is the numerical factor of a term
that contains a variable.
e.g.
4x + 4
In this expression there is only one term that
has a variable and the coefficient is 4.
Equivalent Expressions
A term without a variable is called a constant.
e.g.
4x + 4
Constant.
Equivalent Expressions
Like terms are terms that contain the same
variable. Only like terms can be added or
subtracted.
e.g.
4x + 6 + 5x
Like terms
Equivalent Expressions
To simplify an numeric or algebraic
expression, use properties to write an
equivalent expression that has no like terms
and no parentheses.
Numeric
3 + 3 = 2(3) or 6
Algebraic
x + x = 2x
Equivalent Expressions
Simplify the expression
6(4x)
Equivalent Expressions
Simplify the expression
6(4x)
According to the Associative Property if an
expression has all multiplication or addition,
we can remove the parenthesis.
6·4·x
Can we perform any operation?
Equivalent Expressions
Simplify the expressions
6(4x)
24x
Equivalent Expressions
Simplify the expression
11(3x)
Equivalent Expressions
Simplify the expression
11(3x)
33x
Equivalent Expressions
Simplify the expression
x+x+x
Equivalent Expressions
Simplify the expression
x+x+x
3x
Equivalent Expressions
Simplify the expression
5x + 3x + 6x
Equivalent Expressions
Simplify the expression
5x + 3x + 6x
14x
Equivalent Expressions
Simplify the expression
(14y + x) + 22y
Equivalent Expressions
Simplify the expression
(14y + x) + 22y
According to the Associative Property if an
expression has all multiplication or addition,
we can remove the parenthesis.
14y + x + 22y Can we perform any operation?
Equivalent Expressions
Simplify the expression
(14y + x) + 22y
36y + x
Remember you can only add or subtract like
terms.
Equivalent Expressions
Simplify the expression
3x + (9y + 2x)
Equivalent Expressions
Simplify the expression
3x + (9y + 2x)
5x + 9y
Equivalent Expressions
Simplify the expression
4(2x + y)
Equivalent Expressions
Simplify the expression
4(2x + y)
4 ·2x + 4 · y
8x + 4y
Equivalent Expressions
Simplify the expression
9(3x + 2y)
Equivalent Expressions
Simplify the expression
9(3x + 2y)
9 ·3x + 9 · 2y
27x + 18y
Equivalent Expressions
Simplify the expression
4(3x + 7y)
Equivalent Expressions
Simplify the expression
4(3x + 7y)
4 ·3x + 4 · 7y
12x + 28y
Equivalent Expressions
What is the sum of 4 and a number added to
13 as an expression?
Equivalent Expressions
What is the sum of 4 and a number added to
13 as an expression?
4 + n + 13
17 + n
Equivalent Expressions
What is four sets of the sum a number and 6
as an expression?
Equivalent Expressions
What is four sets of the sum a number and 6
as an expression?
4( n + 6)
4n + 24
Equivalent Expressions
A farmer’s market sells fruit baskets. Each
basket has 3 apples and 1 pear. Use a to
represent the cost of each apple and p to
represent the cost of each pear. Write and
simplify an expression that represents the
What is in each group?
Equivalent Expressions
A farmer’s market sells fruit baskets. Each
basket has 3 apples and 1 pear. Use a to
represent the cost of each apple and p to
represent the cost of each pear. Write and
simplify an expression that represents the
(3a + p)
How many groups are there?
Equivalent Expressions
A farmer’s market sells fruit baskets. Each
basket has 3 apples and 1 pear. Use a to
represent the cost of each apple and p to
represent the cost of each pear. Write and
simplify an expression that represents the
5(3a + p)
Can we simplify?
Equivalent Expressions
A farmer’s market sells fruit baskets. Each
basket has 3 apples and 1 pear. Use a to
represent the cost of each apple and p to
represent the cost of each pear. Write and
simplify an expression that represents the
5(3a + p) =
15a + 5p
Equivalent Expressions
The gift bag from Claire Cosmetics includes
5 bottles of nail polish and 2 tubes of lip
gloss. Use p to represent the cost of each
bottle of nail polish and g to represent the
cost of each tube of lip gloss. Write and
simplify an expression that represents the
total cost of 8 gift bags.
Equivalent Expressions
The gift bag from Claire Cosmetics includes
5 bottles of nail polish and 2 tubes of lip
gloss. Use p to represent the cost of each
bottle of nail polish and g to represent the
cost of each tube of lip gloss. Write and
simplify an expression that represents the
total cost of 8 gift bags.
8(5p + 2g) =
40p + 16g
Equivalent Expressions
A fall candle gift set has 4 vanilla candles and
6 pumpkin spice candles. Use v to represent
the cost of each vanilla candles and p to
represent the cost of each pumpkin spice
candle. Write and simplify an expression that
represents the total cost of 4 sets.
Equivalent Expressions
A fall candle gift set has 4 vanilla candles and
6 pumpkin spice candles. Use v to represent
the cost of each vanilla candles and p to
represent the cost of each pumpkin spice
candle. Write and simplify an expression that
represents the total cost of 4 sets.
4(4v + 6p) =
16v + 24p
Equivalent Expressions
Seven friends have similar cell phone plans.
The price of each plan is \$x. Three of the
seven friends pay an extra \$4 per month for
unlimited texts. Write and simplify and
expression that represents the total cost of
the seven plans.
Equivalent Expressions
Seven friends have similar cell phone plans.
The price of each plan is \$x. Three of the
seven friends pay an extra \$4 per month for
unlimited texts. Write and simplify and
expression that represents the total cost of
the seven plans.
3(x + 4) + 4x =
3x + 12 + 4x =
7x + 12
Equivalent Expressions
Mikayla bought five skirts at \$x each. Three
of the five skirts came with a matching top for
an additional \$9 each. Write and simplify an
expression that represents the total cost of
her purchase.
Equivalent Expressions
Mikayla bought five skirts at \$x each. Three
of the five skirts came with a matching top for
an additional \$9 each. Write and simplify an
expression that represents the total cost of
her purchase.
3(x + 9) + 2x =
3x + 27 + 2x =
5x + 27
Equivalent Expressions
Translate the verbal expression into an
Simplify.
7x + 5(x + 3) + 4x – x - 2
Equivalent Expressions
Translate the verbal expression into an
Simplify.
7x + 5(x + 3) + 4x – x – 2
7x + 5x + 15 + 4x – x – 2
15x + 13
Equivalent Expressions
Translate the verbal expression into an
Simplify.
6 + 2(x – 8) + 3x – 11 + x
Equivalent Expressions
Translate the verbal expression into an
Simplify.
6 + 2(x – 8) + 3x – 11 + x
6 + 2x – 16 + 3x – 11 + x
6x - 21
Equivalent Expressions
Agenda Notes
Homework –
Homework Practice 6.6.7
Due Friday, Nov 7
Chapter 6.6 Test –Monday, Nov 10
Accum Rev 6 due Nov 10
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