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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 + 3 y 2. nty 3. 3 y – t Write an algebraic expression for each word phrase. 4. 5 minutes fewer than m minutes

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exploring two step equations
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 + 3y2.nty3. 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

exploring two step equations1
Exploring Two-Step Equations

COURSE 2 LESSON 2-5

Solutions

1.n + 3y2.nty3. 3y – t

4 + 3(3) 4 • 2 • 3 3(3) – 2

4 + 9 24 9 – 2

13 7

4.m – 5 5. 2p6.d + 5

2-5

exploring two step equations2

Let = length of rope in inches.Define the variable.

4 • + 8Write an algebraic expression.

4 + 8 Rewrite 4 • as 4 .

Let c = weight of cheese in ounces.Define the variable.

• c – 1 Write an algebraic expression.

1

2

c – 1 Simplify.

1

2

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

b. half the weight of the cheese in ounces, minus one ounce

2-5

exploring two step equations3

Let m = the number of marbles.Define the variable.

1

4

• m – 6Write an algebraic expression. Note that the order is different from the order in the word phrase.

m – 6 Simplify.

1

4

Exploring Two-Step Equations

COURSE 2 LESSON 2-5

(continued)

c. six fewer than one fourth of the marbles

2-5

exploring two step equations4

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

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.

  • 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.

2-5

exploring two step equations5

– 4 = 14Cover 9k. Think: What number minus

4 is 14? Answer: 18

9k = 18So , or 9k, must equal 18.

9 • = 18 Think: What number times 9 is 18? Answer: 2

k = 2 So , or k, must equal 2.

Exploring Two-Step Equations

COURSE 2 LESSON 2-5

Solve 9k – 4 = 14 using number sense.

9k – 4 = 14

2-5

exploring two step equations6

Check 9k – 4 = 14 Check your solution in the original equation.

9(2) – 4 14Substitute 2 for k.

18 – 4 14 Simplify.

14 = 14 The solution checks.

Exploring Two-Step Equations

COURSE 2 LESSON 2-5

(continued)

2-5

exploring two step equations7

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
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?

2-5

exploring two step equations8

80 + = 200 Cover 6z. Think: What number added to 80 is 200? Answer: 120.

  • 6z = 120So , or 6z, must equal 120.
  • 6 = 120 Think: What number times 6 is 120? Answer: 20.
  • z = 20 So , or z, must equal 20.
Exploring Two-Step Equations

COURSE 2 LESSON 2-5

(continued)

  • 80 + 6z = 200
  • They will have to save $20 per month.

2-5

exploring two step equations9

g

6

k

3

Exploring Two-Step Equations

COURSE 2 LESSON 2-5

Solve each equation using number sense.

1. 5d + 3 = 53 2. – 4 = 2

3. 7h – 10 = 25 4. + 20 = 31

d = 10

g = 36

h =5

k =33

2-5