Properties
Multiplying over parenthesis is what property?
Distributive Property.
After you list the operations that happened to the variable you must _______ them to solve for the variable.
Reverse/invert/do opposite steps
When a problem says “express x in terms of a, b, and c,” it is telling you to
Isolate x or solve for x
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
3x + y = 9
2x - y = 6
x = 3
y = 0
Rearranging or swapping terms is considered which property?
Commutative Property
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.
Solve for T
PV = nRT
T = (PV)/nR
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
-8x - 10y = 24
12x + 10y = 4
x = 7
y = 8
Grouping terms together or changing where we place our parenthesis is considered what property?
Associative Property
7x – 15 = 20
x = 5
Solve for y
3x - 2y = 18
y = -1.5x + 9
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
2x + y = 7
x = 2y + 6
x = 4
y = -1
When solving w2 - 5 = 8w + 5,
Kate wrote w2 - 10 = 8w.
The property she used is
Subtraction Property
5(x - 3) + 2x = 4(x + 3)
x = 9
Solve for y
-(3/2)x + (1/2)y = -7
y = 3x - 14
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
y = -3x + 5
5x - 4y = -3
x = 1
y = 2
Which operations are not represented by the commutative property?
Subtraction Property / Division Property
-5n - 3(1 - 4n)= 37 - n
n = 5
The amount of energy, Q, in joules, needed to raise temperature of m grams of a substance is given by the formula Q = mC(Tf - Ti), 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?
Tf = Q/(mC) + Ti
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
4x + 5y = 9
-11x - 9y = -20
x = 1
y = 1