Simplifying and Solving Equations

Simplifying Expressions

100

Simplify the following expression: 3x + 9x

12x

200

Simplify the following expression: 4(y + 6) + 9

4y + 33

300

Simplify the following expression: -7(x + 2) + 4x

-3x - 14

400

Simplify the following expression: 8x + 2x - 3y - 9x

x - 3y

500

A triangle has side lengths of 4p, 8 - p, and 3p + 1. Write an expression for the perimeter of the triangle.

6p + 9

Solving Multistep - Level 1

100

Solve for a: 4a + 3 = 11

a = 2

200

Solve for y: 15y + 31 = 61

y = 2

300

Solve for x: 28 = 8x + 12 - 7x

x = 16

400

Solve for x: 2(x + 3) = 10

x = 2

500

Solve for p: 17 = 3(p - 5) + 8

p = 8

Multistep Equation Word Problems

100

Paul bought a student discount card for the bus. The card cost $7 and allows him to buy daily bus passes for $1.50. After one month, Paul spent $29.50. How many daily bus passes did Paul buy?

Paul bought 15 daily bus passes.

200

Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 to her savings. How long will it take her to save enough money to buy the bike?

It will take 15 weeks for Jennifer to save up for the bike.

300

Together Marc and Paoli have $32. Marc has $4 less than twice the amount Paoli has. How much does each man have?

Marc has 12 dollars and Paoli has 20 dollars.

400

Two angles are complementary. One angle is 28 degrees more than the other one. Find the measure of each angle.

Angle 1 = 31 degrees Angle 2 = 59 degrees

500

Takeo drove to a baseball game. His ticket cost $10.50 and parking was $6. Popcorn cost $2.25 a box and Takeo bought 2 boxes. Takeo also bought 1 drink. The baseball game and the snacks cost a total of $24.50. How much did his drink cost?

His drink cost $3.50

Solving Multistep - Level 2

100

Solve for x: 3(x - 1) = 5(2 - 4)

x = -7/3

200

Solve for w: 2(w + 3) = 4/5(10 - 5)

w = -1

300

Solve for y: 15y + 14 = 2(5 + 6)

y = 8/15

400

Solve for d: 4(3d - 2) = 1/8(21 - 5)

d = 5/6

500

Solve for a: 5(5a + 3) = 14 - 29 + 3(3(3))

a = -3/25

Equations with Variables on Both Sides Word Problems

100

Jack and Jessica earned the same amount last week. They both make the same amount per hour. Jack worked eighteen hours and had $42 deducted from his pay. Jessica worked fifteen hours and had $18 deducted from her pay. What was each person’s salary last week after deductions?

Each earned $102 after deductions.

200

Joshua can purchase tile at one store for $0.99 per tile, but he will have to rent a tile saw for $25. At another store he can buy tile for $1.50 per tile and borrow a tile saw for free. Find the number of tiles for which the cost is the same. Round to the nearest tile.

For 49 tiles the cost will be the same for both companies.

300

One plumber charges a fee of $75 per service call plus $15 per hour. Another plumber has no flat fee, but charges $25 per hour. Find the number of hours for which the cost of the two plumbers is the same.

For 7.5 hours of work, both companies will charge the same amount.

400

Carpet Plus installs carpet for $100 plus $8 per square yard of carpet. Carpet World charges $75 for installation and $10 per square yard of carpet. Find the number of square yards of carpet for which the cost including carpet and installation is the same.

12.5 square yards of carpeting will cost the same for both companies.

500

Fifteen more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15. She worked the same number of hours each week. How many hours did she work each week?

She worked for 30 hours both weeks.