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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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


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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

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.

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(continued)


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.

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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.


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


Solve 9k – 4 = 14 using number sense.


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.

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(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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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 80 + (z • 6) = 200

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(continued)

80 + 6z = 200

They will have to save $20 per month.


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.

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Solve each equation using number sense.

1. 5d + 3 = 53 2. – 4 = 2

3. 7h – 10 = 25 4. + 20 = 31

d = 10

h = 5


g = 36

k = 33

g6

k3

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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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