Solving Equations with Distributing and Combining Like Terms

Word Problems

100

An train burns 450 gallons of fuel to get up to speed and then 2.7 gallons of fuel per mile that it travels after that. Write an equation and define your variables. 

2.7x + 450 = y

x is miles

y is total fuel

200

Stacy and her brother and 2 friends are taking a taxi to the zoo.  The cost of the taxi is $5 to start and then $1.35 per mile driven. Write an equation and define  your variables.

1.35x + 5 = y

x is miles

y is total cost

300

Stacy and her brother and 2 friends are taking a taxi to the zoo.  The cost of the taxi is $5 to start and then $1.35 per mile driven.

Stacy has $15 dollars and her brother has $7.  If the zoo is 11 miles away will they have enough money to afford the ride? Prove it. 

y = 1.35 (11) + 5

y = 14.85 + 5

y = 19.85

They have $22. This will be enough. 

400

Each Saturday a gym holds a 45 minute yoga class. On weekdays the classes only last 30 minutes.  Last week there were 165 total minutes of yoga class.

Write an equation to model this situation.  Be sure to define your variables.

30x + 45 = y

30x + 45 = 165

x is week days

y is total minutes 

500

Each Saturday a gym holds a 45 minute yoga class. On weekdays the classes only last 30 minutes. Last week there were 165 total minutes of yoga class.

Use your equation to find out how many Weekday yoga classes were held.

30x + 45 = 165

x = 4 weekdays

Equations with Variables on Both Sides

100

Solve for the variable:

5x = 3x + 20

x = 10

200

Solve for the variable:

6m - 7 = 2m + 25

m = 8

300

Solve for the variable:

10k + 30 = -2k + 54

k = 2

400

Solve for the variable:

-6a + 5 = 3a - 22

a = 3

500

Solve for the variable:

4p + 29 = 5(p + 6)

p = -1

Two-Step Equations

100

Solve for the variable:

2x + 1 = 7

x = 3

200

Solve for the variable:

x/7 - 2 = 4

x = 42

300

Solve for the variable:

8a - 3 = 61

a = 8

400

Solve for the variable:

-9m + 2 = 83

m = -9

500

Solve for the variable:

g/10 + 5 = -1

g = -60

Combining Like Terms

100

Combine like terms:  

2a + 3a + 5a

10a

200

Simplify the expression below:  

-7b+ 11 + 2b

-5b + 11

300

Combine like terms:  

5a + 9 - 3a = -19

a = -14

400

Solve for the variable:

7m + 3m = 70

m = 7

500

Solve for the variable:

3a + 5 - 6a + 2  = -23

a = 10

Distributive Property

100

Simplify:

3(a + 2) 

3a + 6

200

Simplify:

-7(5k - 8)

-35k + 56

300

Write the expression in factored form:  6x + 15y - 24z

3(2x + 5y - 8z)

400

Solve for the variable:

4(2a + 1) = 20

a = 2

500

Solve for the variable:

-5(3y + 2) -8 = -58

y = -4