Expression and Equations

Simplify

100

15m - 9m

6m

200

3p³ + 5p² - p³

2p³ + 5p²

300

2q² + q - 7q - 5p²

-3p² - 6q

400

Simplify.

7(m - 3) + 4(m + 5)

11m + 10

500

3(x² - y) + 9(x² +2y)

12x² + 15y

Word Problems

100

Richie has a lemonade stand in the summer time. Richie sells his cup of lemonade for $1.00. If he had to pay $10 to buy cups and the ingredients to make the lemonade, how many cups will Richie have to sell to make a profit?

11

200

You start driving a used car when the odometer reads 96,882. After a typical month of driving, the reading is 97,057. Write an expression for the reading on the odometer after m months, assuming the amount you drive each month is the same. Predict the reading after 12 months. 

Mileage or M = 175x +96,882

M(12) = 98,982 miles

300

In the United States, the average movie ticket price  (in dollars) since 1974 can be modeled by 0.131x + 1.89 where x is the number of years since 1974. What values of x should you use to find the ticket prices in 1974, 1984, 1994, and 2004? Find the ticket prices for those years.

$1.89

$3.20

$4.19

$5.50

400

A company offers each of its 80 workers either a desktop computer that costs $900 or a laptop that costs $1550. Write and simplify an expressions for the cost of all computers when n workers choose desktop computers. Find the cost if 65 workers choose desktop computers.

Total Cost or C = 900n + 1550(80-n)

C(65) = 900(65) + 1550(80-65)

C(65) = $81,750

500

Under what conditions are the expressions (x+y)² and 

x² + y² equal? Are the expressions equivalent? 

Only where x = 0, The expressions are not equivalent.

Expressions

100

10m + 32 when m = -5

-18

200

Evaluate.

12 + (8 - n)³    when n = 5

39

300

Evaluate.

p³ - 3p²  when p = -2

-20

400

Simplify and Evaluate.

8x + 6x² - 9x² - 4x   where x = 1

-3x² + 4x where x = 1

-3(1)² + 4(1) = 1

500

(10x)/(2z - 3) where x = -3 and z = -6

2

Equations

100

(4/5)x + 8 = 20

x = 15

200

x + 8 = 11

x = 3

300

7 - (5/3)c = 22

c = -9

400

What is the solution of 4x - 7 = -15 ?

x = -2

500

What is the solution of 7t - 5 = 3t + 11

t = 4

Distributive Property

100

Solve.

2(b + 3) = 4b - 2

b = 4

200

Solve.

5b - 4 = 2(b + 4)

b = 4

300

Solve.

3(m - 3) = 6(m + 1)

m = -5

400

Solve.

5d + 17 = 4(d + 3)

d = -5

500

3(2x - 5) - x = -7(x + 3) 

x = -1/2