Chapter 3 - Equations

Combining Like Terms & the Distributive Property

100

8(4 + 6p)

48p +32

200

-5(-7 + 8n)

-40n + 35

300

-(n - 9) + 4

-n + 13 

OR 

-1n + 13

400

3(1 + 2v) - 3(1 + 4v)

-6v

500

10(9 + 8n) - 6(7n + 9)

38n + 36

Multi-Step Equations

100

-12 = 2 + 5v + 2v

v = -2

200

-3(4r - 8) = -36

r = 5

300

-3(1 + 6x) = 14 - x

x = -1

400

-12(x - 12) = -9(1 + 7x)

x = -3

500

-10n + 3(8 + 8n) = -6(n - 4)

n = 0

Turning Repeating Decimals into Fractions

100

Express the decimal 0.5 as a fraction if the repeating number of your decimal is 5.

x = 5/9

200

Express the decimal 0.83 as a fraction if the repeating number of your decimal is 3.

x = 5/6

300

Express the decimal 0.05 as a fraction if the repeating number of the decimal is 5.

x = 1/18

400

Express the decimal 0.21 as a fraction if the repeating numbers of your decimal are 21.

x = 7/33

500

qExpress the decimal 0.231 if the repeating decimal number is 1.

x = 52/225

One Solution, No Solution, or Infinite Solutions?

100

3x + 5 = 2x - 7

x = -12

200

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

-3 = -3

Infinite Solutions

300

0.5(6x - 3) = 3(1 + x)

-1.5 (not)= 3

No Solution

400

1/7(7x - 21) = 8x + 7x - 24

x = -1.5 

OR x = 21/14 

OR x = 1 1/2

500

(x - 3) / 4 = (0.25x - 0.75)

-3 = -3

Infinite Solutions

Equations Grab Bag

100

Find the value of y when x = 2

2x - 1 = y + 4

y = -1

200

Find the value of x when y = -7

1/2 (x+4) = 1/3 (y + 1)

x = -8

300

Find the value of x when y = -7

(2x - 1) / 5 = 2(y + 7) 

x = 1/2

400

Find x in terms of y.

5x - y = 3(x + y)

x = 2y

500

Find x in terms of y. Then, solve for x if y = 5.

2y + 8 = 1/4x

x = 8y + 32

x = 72