Algebraic Expressions

Simplifying

100

Which of the following are like terms?

5x      6y       9        0.5x         x²       3xy      -20x  

5x, 0.5x, and -20x

200

Simplify the following expression:

19 - 35x + 13y + 4 - 33  + -5x

-40x + 13y - 10

300

Sophie buys a bike that costs b dollars. After a 5.5% sales tax is added, the total cost can be expressed by the expression b + 0.055b. What is the expression written in simplest form?

1.055b

500

Simplify the following expression:

3/4x - 3/5y + 7/8x - 1/3y

1 5/8x - 14/15y

500

Simplify the following expression:

1/3(15x - 12) + 5/6x - 12 + 5/9x

6 7/18x - 16

Adding

100

Add the following linear expressions:

(-2x + 5) + (4x - 9)

2x - 4

200

Add the following linear expressions:

(8y + 23) + (-14y - 56)

-6y - 33

300

What is the perimeter of a triangle with the following side lengths?

A. 5x - 9             B.  46           C. 4x + 7

9x + 44

500

A rectangular pool was installed at the Wilson residence. The L=28 yd and W=(3x - 6)yd. What is the perimeter of the pool?

6x + 44

500

(3 5/6y - 1/3) + (1/8 - 3/4y)

3 1/12y - 5/24

Subtracting

100

Subtract the following linear expressions:

(13x + 7) - (5x + 12)

8x - 5

200

Subtract the following linear expressions:

(-9x + 4) - (-4x - 17)

-5x + 21

300

Jaden biked 6n + 3 miles and Micha biked 3n + 5 miles. How many more miles did Jaden bike than Micha?

3n - 2

500

Subtract the following linear expressions:

(5.7x - 13) - (12.4 + 3.4)

6.7x - 16.4

500

(-2/3x + 4/7) - (1 1/2x - 1/3)

-2 1/6x + 19/21

Factoring/Expanding

100

What is the GCF of 10z and 22?

2

200

What is the GCF 81mn and 18n?

9n

300

Expand the following expression:

-7(12x - 4)

-84x + 28

500

Factor the following expression:

88x - 33y

11(8x - 3y)

500

-2/5(10x + 25) - 16

-4x - 26

Linear Expressions

100

Which of the following are linear expressions:

6x    1/2     5xy     -1/3b      (-y + 4)      9x²

6x, 1/2, 1/3b and -y + 4

200

Add the following linear expressions:

(12 + 3x) + (-12 - 14x)

-11x

300

Subtract the following linear expressions:

(2/3x - 19) - (-4/5x -21)

1 2/5x + 2

500

A flower shop sells two different bouquets. The basic costs $16 each and the deluxe costs $24 each. The number of arrangements sold of each after d days are:

Basic = 5d - 3           Deluxe = 3d + 7

After 7 days, how much more did the store earn from deluxe arrangements than basic arrangements? 

$160 more

500

The basketball team is accepting donations and is hosting a car wash to raise money for new equipment. The team will keep 50% of the profits where w is how much each car wash costs. If the team charges $5 per car wash, how much money will the team earn on Saturday and Sunday?

Saturday = 24w + 40          Sunday = 19w + 101

$178