7th - Chapter 3 Review (Part 1)

Equations with Fractions

100

b/8 = 3

b = 24

200

7/9x = 49

7/9x = 49

x = 49 xx 9/7

x = 63

300

1/5x - 2/3 = 7/10

1/5x - 2/3 = 7/10

1/5x = 21/30 + 20/30

1/5x = 41/30

x = 41/30 xx 5

x = 41/6 or 6 5/6

400

c/7 - 9/14 = -17/21

c/7 - 9/14 = -17/21

c/7 = -34/42 + 27/42

c/7 = -7/42

c = -7/42 xx 7

c = -7/6 or -1 1/6

500

-4/3 - 3/5x = -4

-4/3 - 5/3x = -4

-5/3x = -12/3 + 4/3

-5/3x = -8/3

x = -8/3 xx -3/5

x = 8/5 = 1 3/5

Solving by Using the Distributive Property

100

2(x + 5) = 14

2x + 10 = 14

2x = 4

x = 2

200

-5(d - 2) = 40

-5d + 10 = 40

-5d = 30

d = -6

300

7(4 - 3t) = -84

28 - 21t = -98

-21t = -126

t = 6

400

- 2/3 (x - 9) = -24

- 2/3x + 6 = -24 

-2/3x = -30

x = -30 xx -3/2

x = 45

500

3/4(1/6x + 2/9) = 5

1/8x + 1/6 = 5

1/8x = 29/6

x = 29/6 xx 8

x = 116/3 = 38 2/3

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

7h = 21

h = 3

200

3b + 13b - 8 = 40

16b = 48

b = 3

300

3a + 12 - 6a = -9

-3a = -21

a = 7

400

-26 = -3y + 1 + 5y - 11y

-26 = -9y + 1

-27 = -9y

y = 3

500

87 = 3c - 12 - c + 3 + 14c

87 = 12c - 9 

96 = 12c 

8 = c

Variables on both sides

100

d + 16 = 9d

16 = 8d

2 = d

200

33 - 4e = 7e

33 = 11e

3 = e

300

9 - 2x = 4x - 9

18 = 6x

x = 3

400

-9x = -4x + 35

-5x = 35

x = -7

500

 7/9 x - 8  = - 1 +  5/12 x

13/36x=7

x = 7 xx 36/13

x = 252/13 = 19 5/13

Multi-Step Equations

100

4(x + 11) + 13 = 33

4x + 44 + 13 = 33

4x + 57 = 33

4x = -24

x = -6

200

x + 3x + 1 = -8 - 5x

x + 3x + 1 = -8 - 5x 

4x + 1 = -8 - 5x 

9x = -9

x = -1

300

4(y - 2) + y = -13 + 7y - 19

4(y - 2) + y = -13 + 7y - 19

4y - 8 + y = 7y - 32

5y - 8 = 7y = -32

24 = 2y 

y = 12

400

-6(m + 1) + 18 = 2(4 - 5m)

-6(m + 1) + 18 = 2(4 - 5m)

-6m - 6 + 18 = 8 - 10m

-6m + 12 = 8 - 10m

4m = -4

m = -1

500

7k - 8 + 2(k + 12) = 5(2 - 6k) + 6

7k - 8 + 2(k + 12) = 5(2 - 6k) + 6

7k - 8 + 2k + 24 = 10 - 30k + 6

9k + 16 = -30k + 16

39k = 0

k = 0

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Their combined age is 21 years old. How old is her sister?

x + x + 3 = 21

2x + 3 = 21

2x = 18

x = 9 

9 years old

200

Megan bought 7 t-shirts, and she also purchased jeans for $40. Megan spent a total of $117. If each t-shirt cost the same amount, much did each t-shirt cost?

7n + 40 = 117

7n = 77

n = 11

300

Jaime, Jerry, and Herb collect comic books. At a convention, Jaime purchased eight more than Jerry, and Herb purchased 1 less than twice the amount Jaime purchased. If they purchased 63 comic books altogether, how many did Jaime purchase?

Jaime: x + 8,    Jerry: x        Herb: 2(x + 8) - 1

x + 8 + x + 2(x + 8) - 1 = 63

x + 8 + x + 2x + 16 - 1 = 63

4x + 23 = 63

4x = 40 

x = 10,    so Jaime purchased 10 + 8 = 18 comics

400

Gianna LOVES bowling. Can't stop won't stop. The score of her first game was 8 pins less than her second, and the score of her third game was 20 more than her second. The sum of her first two games is 60 more than her third game. What was her total score for all three games?

Game 1: x - 8, Game 2: x, Game 3: x + 20

x - 8 + x = x + 20 + 60

2x - 8 = x + 80

x = 88

80 + 88 + 108 = 276

500

At a fundraiser, cookies cost $1.50, and brownies cost $2. At the end of the day, there were c cookies sold, the number of brownies sold was 7 less than half the amount of cookies. If the fundraiser collected $86 from the sale of cookies and brownies, how many of each treat were sold?

1.5c + 2(1/2c- 7) = 86

1.5c + 1c - 14 = 86

2.5c = 100

c = 40 cookies

1/2(40) - 7 = 20 - 7 = 13 brownies