1-3: Algebraic Expressions
Solve It!
Monday
Tuesday
Walk Dogs
8-9 a.m.
Studio 1-5
p.m.
Wednesday
Thursday
Walk Dogs
8-9 a.m.
Studio 1-5
p.m.
Studio 1-5
p.m.
Friday
Saturday
Walk Dogs
8-9 a.m.
Studio 1-5
p.m.
Studio noon4 p.m.
During summer vacation you work two jobs. You walk three dogs several times a
week and you work part time as a receptionist at a hair studio. You earn $8 per hour as
a receptionist and $20 per week per dog. Your weekly schedule (shown above) is the
same each week. How much will you earn in 10 weeks? Explain.
Example 1:
Which algebraic expression models the word phrase seven fewer than a number t?
a.) t + 7
b.) -7t
c.) t – 7
d.) 7 – t
You Try:
Which algebraic expression models the word phrase two times the sum of a and b?
a.) a + b
b.) 2(a + b)
Algebra 2: 1-3 Algebraic Expressions
c.) 2a + b
d.) a + 2b
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Example 2:
a.) You start with $20 and save $6 each week. What algebraic expression models
the total amount you save?
b.) You had $150 but are spending $2 each day. Write an algebraic expression
that models this situation.
Example 3: What is the value for each expression for the given values of the
variables?
a.) 7(a + 4) + 3b – 8 for a = -4 and b = 5
b.)
𝑥
4
+ 𝑦 2 for x = 1 and y = ½
c.) What is the value of 4(𝑚 − 2) + 3𝑛 + 5 for m = 6 and n = -3?
d.) What is the value of
2(𝑥 2 +𝑦 2 )
3
Algebra 2: 1-3 Algebraic Expressions
for x = 6 and y = -3?
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Example 4: Write and evaluate an expression for each.
a.) In football, a touchdown (TD) is worth 6 points, an extra-point kick (EPK) is
worth 1 point, and a field goal (FG) 3 points. What algebraic expression models
the total number of points that a football team scores in a game, assuming each
scoring play is one of the three given types? Suppose a football team scores 3
touchdowns, 2 extra-point kicks, and 4 field goals. How many points did the team
score?
b.) In basketball, teams can score by making two-point shots, three-point shots,
and one-point free throws. What algebraic expression models the total number of
points that a basketball team scores in one game? If a team makes ten two-point
shots, 5 three-point shots, and 7 free throws, how many points does it score in all?
Example 5: Combine like terms. What is the simplified form of each expression?
a.) 7𝑥 2 + 3𝑦 2 + 2𝑦 2 − 4𝑥 2
b.) −(3𝑘 + 𝑚) + 2(𝑘 − 4𝑚)
c.) −4𝑗 2 − 7𝑘 + 5𝑗 + 𝑗 2
d.) −(8𝑎 + 3𝑏) + 10(2𝑎 − 5𝑏)
Algebra 2: 1-3 Algebraic Expressions
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Challenge!
a.) Combine like terms: −5(2𝑥 3 − 5𝑥 2 + 3𝑥𝑦 + 9𝑥 − 4𝑥𝑦 + 7𝑥 3 − 6𝑥 2 − 𝑥)
b.) Evaluate the expression
(𝑐 2 −𝑑)3 +2𝑎+𝑏2
5(𝑎+𝑑)
for a = 4, b = -2, c = 1, and d = -1
c.) Write an expression that models the following situation:
You ask for your bill at a restaurant. You have a $5 off coupon that will be
applied after the 6% sales tax. Write an expression for the total amount of
money you will pay.
Homework: pp. 22 – 23 => 10 – 20; 23 – 31 odd
Algebra 2: 1-3 Algebraic Expressions
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