COURSE 2 LESSON 2-5
Exploring Two-Step Equations
(For help, go to Lesson 2-1.)
Evaluate each expression for n = 4, t = 2, and y = 3.
1. n + 3y
2. nty
Write an algebraic expression for each word phrase.
4. 5 minutes fewer than m minutes
5. 2 times the number of points p
6. $5 more than d dollars
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3. 3y – t
COURSE 2 LESSON 2-5
Exploring Two-Step Equations
Solutions
1. n + 3y
3. 3y – t
2. nty
4 + 3(3)
4•2•3
3(3) – 2
4+9
24
9–2
13
4. m – 5
7
5. 2p
6. d + 5
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
Define a variable and write an algebraic expression for
each phrase.
a. four times the length of a rope in inches, increased by eight inches
Let
= length of rope in inches.
4 •
4
+ 8
Define the variable.
Write an algebraic expression.
Rewrite 4 •
+ 8
as 4 .
b. half the weight of the cheese in ounces, minus one ounce
Let c = weight of cheese in ounces.
1
•
2
c
1
c
2
– 1
– 1
Define the variable.
Write an algebraic expression.
Simplify.
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
(continued)
c. six fewer than one fourth of the marbles
Let m
= the number of marbles.
Define the variable.
1
• m
4
– 6
Write an algebraic expression.
Note that the order is different
from the order in the word
phrase.
1
m – 6
4
Simplify.
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
To rent a bicycle, you pay a $12 basic fee plus $2 per hour.
Write an equation for the total cost in dollars of a bicycle rental.
Words
cost per
hour
Let
Expression
2
h
times
number of
hours
plus
basic
fee
= number of hours rented. Let C = total cost
•
h
+
12
Now set the expression equal to the total cost to make an equation.
Equation
2h + 12 = C
Multiplying the hours rented by 2 and adding the basic fee = the total cost.
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
Solve 9k – 4 = 14 using number sense.
9k – 4 = 14
– 4 = 14
9k = 18
9 •
= 18
k = 2
Cover 9k. Think: What number minus
4 is 14? Answer: 18
So
, or 9k, must equal 18.
Think: What number times 9 is 18?
Answer: 2
So
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, or k, must equal 2.
COURSE 2 LESSON 2-5
Exploring Two-Step Equations
(continued)
Check 9k – 4 = 14
Check your solution in the original
equation.
9(2) – 4
14
Substitute 2 for k.
18 – 4
14
Simplify.
14 = 14
The solution checks.
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
The Healy family wants to buy a DVD player that costs
$200. They already have $80 saved toward the cost. How much will
they have to save per month for the next six months in order to have
the whole cost saved?
Words
amount
already
saved
Let
Equation
80
z
plus
(amount to
save per
month • 6)
is
$200
=
200
= amount to save per month.
(z • 6)
+
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
(continued)
80 + 6z = 200
80 +
= 200
6z = 120
6
= 120
z = 20
Cover 6z. Think: What number added
to 80 is 200? Answer: 120.
So
, or 6z, must equal 120.
Think: What number times 6 is 120?
Answer: 20.
So
, or z, must equal 20.
They will have to save $20 per month.
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COURSE 2 LESSON 2-5
Exploring Two-Step Equations
Solve each equation using number sense.
1. 5d + 3 = 53
d = 10
3. 7h – 10 = 25
h=5
2. g – 4 = 2
6
g = 36
4. k + 20 = 31
3
k = 33
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