int math 2 section 2-6 1011
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Simplify Variable ExpressionsTRANSCRIPT
SECTION 2-6Simplify Variable Expressions
ESSENTIAL QUESTION
• How do you add, subtract, multiply, and divide to simplify variable expressions?
•Where you’ll see this:
• Sports, finance, photography, fashion, population
VOCABULARY
1. Order of Operations:
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbols
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponents
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponentsultiplication
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponentsultiplicationivision
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponentsultiplicationivision } from left to right
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponentsultiplicationivisionddition
} from left to right
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponentsultiplicationivisiondditionubtraction
} from left to right
VOCABULARY
1. Order of Operations: Allows for us to solve problems to consistently achieve the same answers
GEMDAS
rouping symbolsxponentsultiplicationivisiondditionubtraction
} from left to right
}from left to right
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
4x + 4y − 7x + 7y
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
4x + 4y − 7x + 7y
−3x +11y
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
4x + 4y − 7x + 7y
−3x +11y
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
4x + 4y − 7x + 7y
−3x +11y
2mn + 2m − 5mn + 5n
EXAMPLE 1
Simplify.
a. 5(x + 3)+ 2x b. 2x − 5(x −1)
c. 4(x + y)− 7(x − y) d. 2(mn + m)− 5(mn − n)
5x +15 +2x
7x +15 2x −5x +5
−3x + 5
4x + 4y − 7x + 7y
−3x +11y
2mn + 2m − 5mn + 5n
2m − 3mn + 5n
EXAMPLE 2
The ticket prices at Matt Mitarnowski’s Googolplex are $8.00 for regular admission and $5.50 for students and seniors. For Saturday’s first show, 350 tickets were sold. Write and simplify a variable expression for the total
admission fees of the tickets for that show.
EXAMPLE 2
The ticket prices at Matt Mitarnowski’s Googolplex are $8.00 for regular admission and $5.50 for students and seniors. For Saturday’s first show, 350 tickets were sold. Write and simplify a variable expression for the total
admission fees of the tickets for that show.
How many regular admission tickets were sold?
EXAMPLE 2
The ticket prices at Matt Mitarnowski’s Googolplex are $8.00 for regular admission and $5.50 for students and seniors. For Saturday’s first show, 350 tickets were sold. Write and simplify a variable expression for the total
admission fees of the tickets for that show.
How many regular admission tickets were sold?r = regular tickets sold
EXAMPLE 2
The ticket prices at Matt Mitarnowski’s Googolplex are $8.00 for regular admission and $5.50 for students and seniors. For Saturday’s first show, 350 tickets were sold. Write and simplify a variable expression for the total
admission fees of the tickets for that show.
How many regular admission tickets were sold?r = regular tickets sold
How many student and senior tickets were sold?
EXAMPLE 2
The ticket prices at Matt Mitarnowski’s Googolplex are $8.00 for regular admission and $5.50 for students and seniors. For Saturday’s first show, 350 tickets were sold. Write and simplify a variable expression for the total
admission fees of the tickets for that show.
How many regular admission tickets were sold?r = regular tickets sold
How many student and senior tickets were sold?
350 − r
So what was the total?
So what was the total?
8.00r + 5.50(350 − r )
So what was the total?
8.00r + 5.50(350 − r )
8.00r +1925− 5.50r
So what was the total?
8.00r + 5.50(350 − r )
8.00r +1925− 5.50r
2.50r +1925
So what was the total?
8.00r + 5.50(350 − r )
8.00r +1925− 5.50r
2.50r +1925
The total admission fees were 2.50r + 1925 dollars
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
a. Two consecutive pages have a sum of 175. What are the pages?
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =174
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =1742 2
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =1742 2 n = 87
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =1742 2 n = 87
87 is the first page, 88 is the next.
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =1742 2 n = 87
87 is the first page, 88 is the next.
Check:
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =1742 2 n = 87
87 is the first page, 88 is the next.
Check: 87+88=
EXAMPLE 3If a page in a book is numbered n, what is the
number of the next page?
n + 1a. Two consecutive pages have a sum of 175. What
are the pages?
n + (n +1) =175
2n +1=175 −1 −1 2n =1742 2 n = 87
87 is the first page, 88 is the next.
Check: 87+88=175
EXAMPLE 3b. Three consecutive pages have a sum of 768.
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 765
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 7653 3
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 7653 3 n = 255
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 7653 3 n = 255
The pages are 255, 256, and 257.
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 7653 3 n = 255
The pages are 255, 256, and 257.
Check:
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 7653 3 n = 255
The pages are 255, 256, and 257.
Check: 255+256+257=
EXAMPLE 3b. Three consecutive pages have a sum of 768.
n + (n +1)+ (n + 2) = 768
3n + 3 = 768 −3 −3 3n = 7653 3 n = 255
The pages are 255, 256, and 257.
Check: 255+256+257=768
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
Shaded area = Larger area - smaller area
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
Shaded area = Larger area - smaller area
A = 5 6(x + 5)⎡⎣ ⎤⎦ − 3 3(x − 4)⎡⎣ ⎤⎦
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
Shaded area = Larger area - smaller area
A = 5 6(x + 5)⎡⎣ ⎤⎦ − 3 3(x − 4)⎡⎣ ⎤⎦
A = 5 6x + 30⎡⎣ ⎤⎦ − 3 3x −12⎡⎣ ⎤⎦
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
Shaded area = Larger area - smaller area
A = 5 6(x + 5)⎡⎣ ⎤⎦ − 3 3(x − 4)⎡⎣ ⎤⎦
A = 5 6x + 30⎡⎣ ⎤⎦ − 3 3x −12⎡⎣ ⎤⎦
A = 30x +150 − 9x + 36
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
Shaded area = Larger area - smaller area
A = 5 6(x + 5)⎡⎣ ⎤⎦ − 3 3(x − 4)⎡⎣ ⎤⎦
A = 5 6x + 30⎡⎣ ⎤⎦ − 3 3x −12⎡⎣ ⎤⎦
A = 30x +150 − 9x + 36
A = 21x +186
EXAMPLE 4Find the area of the shaded region.
3(x − 4)
3 5
6(x + 5)
Shaded area = Larger area - smaller area
A = 5 6(x + 5)⎡⎣ ⎤⎦ − 3 3(x − 4)⎡⎣ ⎤⎦
A = 5 6x + 30⎡⎣ ⎤⎦ − 3 3x −12⎡⎣ ⎤⎦
A = 30x +150 − 9x + 36
A = 21x +186 units2
PROBLEM SET
PROBLEM SET
p. 78 #1-37 odd
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