1. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
(For help, go to Lesson 2-1.)
Evaluate each expression for n = 4, t = 2, and y = 3.
1. n + 3y 2. nty 3. 3y – t
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
2-5

2. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
Solutions
1. n + 3y 2. nty 3. 3y – t
4 + 3(3) 4 • 2 • 3 3(3) – 2
– 2
4. m – p 6. d + 5
2-5

3. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
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. Define the variable.
4 • Write an algebraic expression.
Rewrite 4 • as 4 .
b. half the weight of the cheese in ounces, minus one ounce
Let c = weight of cheese in ounces. Define the variable. 1 2
• c – Write an algebraic expression.
c – Simplify. 1 2
2-5

4. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
(continued)
c. six fewer than one fourth of the marbles
Let m = the number of marbles. Define the variable. 1 4
• m – Write an algebraic expression Note that the order is different from the order in the word phrase.
m – Simplify. 1 4
2-5

5. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
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 times number of plus basic
hour hours fee
Let h = number of hours rented. Let C = total cost
Expression • h
Now set the expression equal to the total cost to make an equation.
Equation h = C
Multiplying the hours rented by 2 and adding the basic fee = the total cost.
2-5

6. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
Solve 9k – 4 = 14 using number sense.
9k – 4 = 14
– 4 = Cover 9k. Think: What number minus
4 is 14? Answer: 18
9k = So , or 9k, must equal 18.
9 • = Think: What number times 9 is 18? Answer: 2
k = 2 So , or k, must equal 2.
2-5

7. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
(continued)
Check 9k – 4 = 14 Check your solution in the original equation.
9(2) – Substitute 2 for k.
18 – Simplify.
14 = 14 The solution checks.
2-5

8. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
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 plus (amount to is $200
already save per
saved month • 6)
Let z = amount to save per month.
Equation (z • 6) =
2-5

9. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
(continued)
z = 200
= Cover 6z. Think: What number added to 80 is 200? Answer: 120.
6z = So , or 6z, must equal 120.
= Think: What number times 6 is 120? Answer: 20.
z = So , or z, must equal 20.
They will have to save $20 per month.
2-5

10. Exploring Two-Step Equations
COURSE 2 LESSON 2-5
Solve each equation using number sense.
1. 5d + 3 = – 4 = 2
3. 7h – 10 = = 31 g 6
d = 10
g = 36 k 3
h = 5
k = 33
2-5