Properties
(Quiz: #1)
(Quiz: #1)
2x + 7 = 17 --> Given Equation
2x + 7 - 7 = 17 - 7 --> WHAT PROPERTY GOES HERE??
Subtraction Property of Equality
18 = 4y + 2y
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
18 = 6y
3(3x - 8) = 21
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
9x - 24 = 21
-6(v + 1) = 2(1 - 3v) - 7
Choose the statement that describes its solution.
No Solution
All real numbers are solutions
v = ?? (if you select this one, you must state the full answer)
No Solution
An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 1200 meters, and Plane B was at an altitude of 816 meters. Plane A is gaining altitude at 10 meters per second, and Plane B is gaining altitude at 18 meters per second.
Let x be the number of seconds that have passed.
(a)For each plane, write an expression for the altitude of the plane after x seconds.
Altitude of Plane A (in meters)= ____________
Altitude of Plane A (in meters)= ____________
(b)Write an equation to show when the two planes would be at the same altitude.
____________ <-- WHAT IS THIS EQUATION?
1200 + 10x = 816 + 18x
12w = -36 --> Given Equation
12w/12 = -36/12 --> WHAT PROPERTY GOES HERE??
Division Property of Equality
8x - 18 - 12x = -62
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
-4x - 18 = -62
-4 = 2u + 3(u - 2)
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
-4 = 2u + 3u - 6
8(x - 1) - 4 = 4(2x - 3)
Choose the statement that describes its solution.
No Solution
All real numbers are solutions
v = ?? (if you select this one, you must state the full answer)
All real numbers are solutions
Aldo received a gift card of $60 for a pizza restaurant. The restaurant charges $5 per pizza. Carmen received a gift card of $100 for a different pizza restaurant. The restaurant charges $10 per pizza.
Let x be the number of pizzas purchased.
(a)For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
Amount of money left on Aldo's card (in dollars) = ____________
Amount of money left on Carmen's card (in dollars) = ____________
(b)Write an equation to show when the two cards would have the same amount of money left on them.
____________ <-- WHAT IS THIS EQUATION?
60 - 5x = 100 - 10x
-5(2v + 6) = 10 --> Given Equation
-10v - 30 = 10 --> WHAT PROPERTY GOES HERE??
Distributive Property
6w + 40 = 14w
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
40 = 8w
-9(w - 2) = -6w + 48
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
-9w + 18 = -6w + 48
3(v + 2) + v = 4(v - 1) + 10
Choose the statement that describes its solution.
No Solution
All real numbers are solutions
v = ?? (if you select this one, you must state the full answer)
All real numbers are solutions
Diane will choose between two restaurants to purchase pizzas for her party. The first restaurant charges a delivery fee of $4 for the entire purchase and $11 per pizza. The second restaurant has no delivery fee and charges $12 per pizza.
Let x be the number of pizzas purchased.
(a)For each restaurant, write an expression for the total charge of purchasing x pizzas (with delivery).
Total charge from the first restaurant (in dollars) = ____________
Total charge from the second restaurant (in dollars) = ____________
(b)Write an equation to show when the total charge (with delivery) would be the same for each restaurant.
____________ <-- WHAT IS THIS EQUATION?
4 + 11x = 12x
(y-7) / 2 = -11 --> Given Equation
2 * (y-7) / 2 = -11 * 2 --> WHAT PROPERTY GOES HERE??
Multiplication Property of Equality
-5x + 6 = -12x + 62
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
7x + 6 = 62
-OR-
6 = -7x + 62
7 + 4(2x - 3) = -2(4x - 4) + 4x
What would the next line look like in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
7 + 8x - 12 = -8x + 8 + 4x
2(u - 3) - 5u = -3(u + 3)
Choose the statement that describes its solution.
No Solution
All real numbers are solutions
v = ?? (if you select this one, you must state the full answer)
No Solution
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $9 monthly fee and charges an additional $0.18 for each minute of calls. The second plan has a $15 monthly fee and charges an additional $0.14 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
_____ minutes
150 minutes
On HW #6 Questions 1 and 2, what "Reason" did you have to select after selecting either the Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, and Division Property of Equality.... BUT NOT after Distributive Property?
Simplifying
-4(4y -6) +8y = 6(y+3)
What would the line look like AFTER FINISHING STEP 5 in solving this equation?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
-14y + 24 = 18
-OR-
24 = 14y + 18
*Note: For this problem, anything you see in ( ) should be written as a fraction
(5/2) y - 3 = - (3/5)y - 7/5
What would this equation look like after completing step 4 and getting rid of all of the fractions?
*Note: you must perform the steps in the order taught in class by Ms. Haumesser
25y - 30 = -6y - 14
-OR-
125y - 150 = -30y - 70
-4(y + 2) + 2 = 2(y + 6)
Choose the statement that describes its solution.
No Solution
All real numbers are solutions
v = ?? (if you select this one, you must state the full answer)
y = -3
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $67,317. The variable costs will be $9 per book. The publisher will sell the finished product to bookstores at a price of $23.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
_____ books
4,724 books