Unit 2 - Expressions

Word Problems

100

The art club wants to order t-shirts. The t-shirts cost $8.50 each, plus a shipping fee of $6. Write an expression that shows the total cost of x t-shirts.

8.5x + 6

200

You need to buy sodas for a meeting you are planning at school. If you need 2 sodas per x students, plus the $16 you need for snacks, write an expression for how much money you spend for x students.

2x + 16

300

You want to rent a paddle board. You have to pay a $5 free for the equipment, plus the company charges $12 an hour. Write an expression that shows how much money will you spend for x amount of hours.

12x + 5

400

Bryce paid $(3x + 8) for a beef roast and $(2x - 4) for potatoes. Write an expression that shows how much money he spend in total.

5x + 4

500

John needs to cut a wood board into 2 pieces. One of the pieces needs to be (12x - 1)feet long. If the whole board is (26x + 7)feet long, how long will the other piece be.

14x + 6

Expressions from Tables

100

Jane meditates 14 hours every month. She wants to meditate more and starts recording her progress. In month 1, she meditates 24 hours, in month 2, 34 hours, in month 3, 44 hours. Write an expression that shows how many hours in a month she meditates.

10x + 14

200

Marvin usually only drinks 16oz of water a day. He wants to drink more, so he start recording is progress. On day 1, he drinks 20 oz of water, on day 2, 24 oz, on day 3, 28 oz. Write an expression that shows how many water he drink in a day.

4x + 16

300

Julia planted a tree in her backyard that is 2.5 feet tall. She measures the height each week and finds that after 1 week, it is 2.6 feet tall, after 2 weeks it is 2.7 feet tall, and after 3 weeks it is 2.8 feet tall. Write an expression that shows the height of the plant.

0.1x + 2.5

400

Greg is trying to lose some weight. On the first day of his diet, he eats 1900 calories. On the second day he eats 1825 calories. On the third day, 1750 calories. Write an expression that shows how many calories he will eat on any given day.

-75x

500

Some scientists have 36 grams of radioactive material. They study how much it decays over several months. After 1 month only 33 grams remain. After 2 months only 30 grams remain. After 3 months only 27 grams remain. Write an expression that shows how many grams of material remain.

-3x + 36

Add and Sub. Polynomials

100

(x + 3) + (3x - 1)

4x + 2

200

(4x) - (x +10)

3x + 10

300

(5x² + 9x - 2) - (3x² - 6)

2x² + 9x + 4

400

(12x³ + 8x² - 6x + 1) + (3x² + x - 10)

12x³ + 11x² - 5x - 9

500

(x⁴ + 9x³ - 12x + 23) + (6x⁴ - 2x³ + x² + 6x)

7x⁴ + 7x³ + x² - 6x + 23

Distribution

100

2(x + 3)

2x + 6

200

5(2x + 13)

10x + 65

300

3x(x - 9)

3x² - 27x

400

5x(-3x + 10)

-15x² + 50x

500

x²(5x + 3)

5x³ + 3x²

Multiplying Binomials

100

(x + 2) (x + 7)

x² + 9x + 14

200

(x + 3) (x - 8)

x² - 5x - 24

300

(2x + 9) (x + 1)

2x² + 11x + 9

400

(4x + 10) (3x + 24)

12x² + 126x + 2400

500

(-6x - 7) (x - 4)

-6x² + 17x + 28