Name ________________________________________ Date __________________ Class __________________
LESSON
2-1
Modeling with Expressions
Reteach
A numerical expression contains
operations and numbers.
4 + 3 − 1 is a numerical expression.
An algebraic expression contains
operations, numbers, and at least one
variable.
5x + 3 − 7y is an algebraic expression.
Terms are the parts of the expression
that are separated by addition signs.
Rewrite subtraction to show addition.
Rewrite 5x + 3 − 7y to show addition:
5x + 3 + (−7y).
The terms are 5x, 3, and −7y.
A coefficient is a number that
multiplies a variable.
5 is the coefficient of x.
−7 is the coefficient of y.
3 does not multiply a variable, so it is
not a coefficient.
Example
Write an expression that reflects the situation.
Jacques has 8 more DVDs than Erik. Write an expression for the
number of DVDs Jacques has.
Erik has d DVDs. Jacques has 8 more DVDs. The word “more”
shows addition.
Jacques has d + 8 DVDs.
Write an expression for each situation.
1. Enrique collected 7 more than 2 times as many recyclable bottles, b,
as Natasha collected. Write an expression for the number of bottles
Enrique collected in all.
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2. Mr. McKay bought b boxes of crackers for $3 each and p pounds of
cheese for $4 per pound. How much did he spend in all?
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3. Jean walked 1 mile to her friend’s house, and then bicycled for 2 hours
at m miles per hour. Write an expression for the total length of her trip.
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Answer Key
Reteach 2-2: Creating and Solving
Equations
Reteach 1-1: Solving Equations
1. x + (−7) = 12; x = 19
2. y + 1 = −5; y = −6
1. m + 2 m = 18; Mako runs 6 miles.
3. −4 = p + (−2); p = (−2)
2. 18 + 0.15 m = 29.25; 75 min
4. −7 = 4 + (−a); a = 11
3.
5. k = −16
6. g = −6
e + (3e − 20)
= 50; Eric collected $30,
2
and Charlotte collected $70.
Reteach 2-3: Solving for a Variable
7. h = −3
8. d = 19
Reteach 1-2: Modeling Quantities
3 ft
1.
1 yd
1m
2.
100 cm
1. b =
2A
h
2. l =
A
w
3. s =
2R + 6t − 5
2
4. c = P −a −b
3.
8 fl oz
1c
5. t =
4.
1000 m 3,391,100 m
m
;
; 40612
1 km
83.5 h
h
6. H =
5. 320
2I
pr
GK
J
7. n = 360 −m − p −q
c
min
Reteach 1-3: Reporting with Precision
and Accuracy
1. 180 min
2. 7.65 g
8. s =
t
r +1
9. a =
bc
d
Reteach 2-4: Creating and Solving
Inequalities
3. 2.50 in.
1. −3e − 10 ≤ −4
−3e − 10 + 10 ≤ −4 + 10
−3e ≤ 6
−3e 6
≤
−3 −3
e ≥ −2
4. 7.203 qt
5. 3 c
6. 35.4 yd
7. 4.9 oz
8. 42 mi
Reteach 2-1: Modeling with
Expressions
1. 2b + 7
2. 3b + 4p
3. 1 + 2m
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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