8th - Multi-step Equations Review

Insultingly Easy Equations

100

b/-8 = 3

b = -24

200

x + 24 = 13

x = - 11

300

1/6 + 5a = 1

1/6 + 5a = 1

5a = 5/6

a = 1/6

400

c/7 - 23 = -20

c/7 - 23 = -20

c/7 = 3

c = 21

500

- 9 - 9x = -9 

-9 - 9x = -9

-9x = 0

x = 0

Solving by Using the Distributive Property

100

2(x + 5) = 14

2(x + 5) = 14

2x + 10 = 14

2x = 4

x = 2

200

5(d - 2) = 40

5(d - 2) = 40

5d - 10 = 40

5d = 50

d = 10

300

7(4 - t) = -84

7(4 - t) = -84

28 - 7t = -84

-7t = -112

t = 16

400

-2(x - 9) = -24

-2(x - 9) = -24

-2x + 18 = -24

-2x = -42

x = 21

500

(4 + 2a)(-13) = 208

(4 + 2a)(-13) = 208

-52 - 26a = 208

-26a = 260

a = -10

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

5h + 2 + 2h = 23

7h + 2 = 23

7h = 21

h = 3

200

3b + b - 8 = 4

3b + b - 8 = 4

4b - 8 = 4

4b = 12

b = 3

300

3a + 13 - 6a = -11

3a + 13 - 6a = -11

-3a + 13 = -11

-3a = -24

a = 8

400

-6 = -3y + 4 + 5y

-6 = -3y + 4 + 5y

-6 = 2y + 4

-10 = 2y

y = -5

500

78 = 3c + 12 - c + 4

78 = 3c + 12 - c + 4

78 = 2c + 16

62 = 2c

c = 31

Solving Equations with Variables on Both Sides

100

d + 16 = 9d

d + 16 = 9d

16 = 8d

d = 2

200

33 - 4e = 7e

33 - 4e = 7e

33 = 11e

e = 3

300

5x + 7 - 2x = 4x - 9

5x + 7 - 2x = 4x - 9

3x + 7 = 4x - 9

7 = x - 9

16 = x

400

2x + 9 - 6x = -4x + 9

2x + 9 - 6x = -4x + 9

-4x + 9 = -4x + 9

9 = 9 True

All reals

500

14x - 33 - 6x = 2x - 1 + 6x

14x - 33 - 6x = 2x - 1 + 6x

8x - 33 = 8x - 1

-33 = -1 False

No Solution

Equation Grab Bag

100

4x + 9 = 3(3 - x)

4x + 9 = 3(3 - x)

4x + 9 = 9 - 3x

7x + 9 = 9

7x = 0

x = 0

200

x + 3x + 12 = -8(1 + 2x)

x + 3x + 12 = -8(1 + 2x)

4x + 12 = -8 - 16x

20x + 12 = -8 

20x = -20

x = -1

300

4(y - 2) + y = -13

4(y - 5) + y = -13

4y - 20 + y = -13

5y - 20 = -13

5y = 7

y = 7/5 

400

-6(m + 1) + 18 = 24 - 2(m + 5)

-6(m + 1) + 18 = 24 - 2(m + 5)

-6m - 6 + 18 = 24 - 2m - 10

-6m + 12 = -2m + 14

-4m = 2

m = -1/2

500

7k - 8 = -k + 52 - 2(k + 12) + 10k

7k - 8 = -k + 52 - 2(k + 12) + 10k

7k - 8 = -k + 52 - 2k - 24 + 10k

7k - 8 = 7k + 28

-8 = 28 False

No solution

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

x + 3 = 11

Julie's sister is 8

200

Mr. Cushman bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How much did each t-shirt cost?

7x = 90.93

x = $12. 79

300

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

4x - 3 = 109

4x = 112

x = 38 apples

400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?

17x + 2.97 = 34.76

17x = 31.79

x = $1.87

500

When you count by ones, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + n + 1 + n + 2 = 48

3n + 3 = 48

3n = 45

n = 15

15, 16, 17