Properties
Solving Equations
Rewriting Equations
Creating Equations
Solving Systems
100

Multiplying over parenthesis is what property?

Distributive Property.

100

After you list the operations that happened to the variable you must _______ them to solve for the variable. 

Reverse/invert/do opposite steps 

100

When a problem says “express x in terms of a, b, and c,” it is telling you to 

Isolate x or solve for x

100

Bryan's hockey team is purchasing jerseys. The company charges $250 for a onetime set-up fee and $23 for each printed jersey. Write an expression that represents the total cost of x number of jerseys for the team?

23x + 250 

100

3x + y = 9

2x - y = 6

x = 3

y = 0


200

Rearranging or swapping terms is considered which property?

Commutative Property

200

List out the 5 steps to solving linear equations.

Distribution Property

Combine Like Terms

Add/Sub Property (move x's to one side)

Add/Sub Property (move constants to other side)

Multi/Division Prop.

200

Solve for T

PV = nRT

T = (PV)/nR

200

At a local garden shop, the price of plants includes sales tax. The cost of 4 large plants and 8 medium plants is $40.

If L is the cost of a large plant and M is the cost of a medium plant, write an equation that models this situation.

4L + 8M = 40

200

-8x - 10y = 24

12x + 10y = 4

x = 7

y = 8

300

Grouping terms together or changing where we place our parenthesis is considered what property?

Associative Property

300

7x – 15 = 20

x = 5 

300

Solve for y

3x - 2y = 18

y = -1.5x + 9

300

Aidan and his sister Ella are having a race. Ella runs at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of the starting line. 

Let y represent the distance from the starting line and x represent the time elapsed, in seconds.

Write an equation to model the distance Ella traveled.

y = 6x + 30

300

2x + y = 7

x = 2y + 6

x = 4

y = -1

400

When solving w2 -  5 = 8w + 5, 

Kate wrote w2 - 10 = 8w. 

The property she used is

Subtraction Property 

400

5(x - 3) + 2x = 4(x + 3)  

x = 9

400

Solve for y

-(3/2)x + (1/2)y = -7

y = 3x - 14

400

At an amusement park, the cost for an adult admission is a, and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95. All ticket prices include tax. 

Write a system of equations, in terms of a and c, that models this situation.

4a + 2c = 325.94

2a + 3c = 256.95

400

y = -3x + 5

5x - 4y = -3

x = 1

y = 2

500

Which operations are not represented by the commutative property?

Subtraction Property / Division Property 

500

-5n - 3(1 - 4n)= 37 - n

n = 5

500

The amount of energy, Q, in joules, needed to raise temperature of m grams of a substance is given by the formula Q = mC(TfTi), where C is the specific heat capacity of the substance. If its initial temperature is Ti, what equation can you use to find its final temperature, Tf?

T= Q/(mC) + Ti

500

Jim had a bag of coins. The number of nickels, n, and the number of quarters, q, totaled 28 coins. The combined value of the coins was $4. 

Write a system of equations that models this situation.

n + q = 28

0.05n + 0.25q = 4

500

4x + 5y = 9

-11x - 9y = -20

x = 1

y = 1

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