2-5 course 2 lesson 2-5 (for help, go to lesson 2-1.) evaluate each expression for n = 4, t = 2, and...
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2-5
COURSE 2 LESSON 2-5COURSE 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
Exploring Two-Step Equations
Solutions
1. n + 3y 2. nty 3. 3y – t
4 + 3(3) 4 • 2 • 3 3(3) – 2
4 + 9 24 9 – 2
13 7
4. m – 5 5. 2p 6. d + 5
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
2-5
Exploring Two-Step Equations
Define a variable and write an algebraic expression for
each phrase.
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
a. four times the length of a rope in inches, increased by eight inches
4 + 8 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.
12 • c – 1 Write an algebraic expression.
c – 1 Simplify.12
Let = length of rope in inches. Define the variable.
4 • + 8 Write an algebraic expression.
2-5
Exploring Two-Step Equations
(continued)
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
c. six fewer than one fourth of the marbles
m – 6 Simplify.14
Let m = the number of marbles. Define the variable.
14 • m – 6 Write an algebraic expression.
Note that the order is different
from the order in the word
phrase.
2-5
Exploring Two-Step Equations
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.
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.
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
Words cost per times number of plus basic hour hours fee
Let h = number of hours rented. Let C = total cost
Expression 2 • h + 12
Exploring Two-Step Equations
Solve 9k – 4 = 14 using number sense.
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
9k – 4 = 14
– 4 = 14 Cover 9k. Think: What number minus
4 is 14? Answer: 18
9 • = 18 Think: What number times 9 is 18?
Answer: 2
k = 2 So , or k, must equal 2.
9k = 18 So , or 9k, must equal 18.
2-5
Exploring Two-Step Equations
(continued)
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
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.
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?
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
Words amount plus (amount to is $200 already save per saved month • 6)
Let z = amount to save per month.
Equation 80 + (z • 6) = 200
2-5
Exploring Two-Step Equations
(continued)
80 + 6z = 200
They will have to save $20 per month.
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
80 + = 200 Cover 6z. Think: What number added to 80 is 200? Answer: 120.
6z = 120 So , or 6z, must equal 120.
6 = 120 Think: What number times 6 is 120? Answer: 20.
z = 20 So , or z, must equal 20.
2-5
Exploring Two-Step Equations
Solve each equation using number sense.
1. 5d + 3 = 53 2. – 4 = 2
3. 7h – 10 = 25 4. + 20 = 31
d = 10
h = 5
COURSE 2 LESSON 2-5COURSE 2 LESSON 2-5
g = 36
k = 33
g6
k3
2-5
Exploring Two-Step Equations
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