2. Solve the following inequality and graph your solution on a number line. Show all your work.

Transcription

1 1. Solve the following inequality and graph your solution on a number line. Show all your work. 2. Solve the following inequality and graph your solution on a number line. Show all your work. 12 3x 4 < 0 15 (x + 7) 4 3. Solve the following inequality and graph your solution on a number line. Show all your work. 4. Solve the following inequality and graph your solution on a number line. Show all your work. 32 2x (x + 5) > 17 #1 x > 4 #2 x 4 #3 x 4 #4 x < 14

2 The function S(t) = t represents the price of a pizza at Sal s Pizza Shack based on how many toppings a customer wants. 1. Evaluate S(5). Explain what this means in the context of the problem. The function S(t) = t represents the price of a pizza at Sal s Pizza Shack based on how many toppings a customer wants. 2. Solve S(t) = 12. Explain what this means in the context of the problem. The function S(t) = t represents the price of a pizza at Sal s Pizza Shack based on how many toppings a customer wants. 3. Evaluate S(3). Explain what this means in the context of the problem. The function S(t) = t represents the price of a pizza at Sal s Pizza Shack based on how many toppings a customer wants. 4. Solve S(t) = Explain what this means in the context of the problem. #1 S(5) =11.50; The pizza will cost $11.50 with 5 toppings. #2 S(6) = 12; The pizza will cost $12 with 6 toppings. #3 S(3) = 10.50; The pizza will cost $10.50 with 3 toppings. #4 S(9) = 13.50; The pizza will cost $13.50 with 9 toppings.

3 It costs 20 dollars to get into the North Carolina State Fair and 2 dollars for each ride. The South Carolina State Fair costs only 10 dollars to get in but 3 dollars for each ride. How many rides would you have to ride to spend the same amount of money at each fair? You and your little sister are going trick or treating. Your sister started of without any candy in her bag but gets 6 pieces at every house. You start off with 30 pieces from school but only get 1 piece from each house. How many houses do you have to visit until your sister has the same amount of candy as you? You want to buy custom t-shirts for every member of your math class. Company 1 tells you that the price of the t-shirts will be calculated by using the function y= 4x+ 52. Company 2 calculates cost using the function y = 10x How many people would you need to order t-shirts for in order for company two to cost less? Neighbors Sara and Nicole are both selling lemonade in their neighborhood. Sara s mom gave her $4.75 to get started and Sara is selling cups of lemonade for 75 cents. Nicole s mom gave her $8.25 and Nicole is selling lemonade for 25 cents a cup. How many cups do the girls have to sell so that Sara has earned more money? #1 x = 10; You would have to ride 10 rides to spend the same amount at each fair. #2 x = 6; You would have to visit 6 houses to have the same amount of candy. #3 x < 7; Less than seven people would need to order T-shirts for Company 2 to be cheaper. #4 x > 7; The girls need to sell more than seven cups for Sara to make more money than Nicole.

4 1. Solve the following equation and check your solution. Show all your work. 2. Solve the following equation and check your solution. Show all your work a 2 = 2(5 4a) 5y 3 = 4y Solve the following equation and check your solution. Show all your work. 4. Solve the following equation and check your solution. Show all your work x 5 = 2(x + 6) 5 3(2m 4) = 7m + 2 #1 a = 1 2 #2 y = 5 #3 x = 9 #4 m = 15

5 1. Solve the following equation by BALANCING and check your solution. Show all your work. 0.5x = Solve the following equation by BALANCING and check your solution. Show all your work. 15 (2x 3) = 9 3. Solve the following equation by BALANCING and check your solution. Show all your work. 1 x + 11 = Solve the following equation by BALANCING and check your solution. Show all your work. 4(x 1) 3 5 = 23 #1 x = 9 #2 x = 4.5 #3 x = 90 #4 x = 22

6 1. Solve the following equation by undoing operations in an UNDO TABLE. 2. Solve the following equation by undoing operations in an UNDO TABLE. (7 4x) 3 = 3 6 = 4( 6x 3) 2 3. Solve the following equation by undoing operations in an UNDO TABLE. 4. Solve the following equation by undoing operations in an UNDO TABLE. 2 = (x + 4) 4 7 = (p 8) 2 #1 x = 4 #2 x = 0 #3 x = 4 #4 x = 6

7 The function f(x) = 10x represents total sales of tickets on opening night of a play. 1. Write and solve an inequality that represents how many tickets would need to be sold to earn total sales of at least $1100. The function f(x) = 10x represents total sales of tickets on opening night of a play. 2. Solve f(x) What does this mean in the context of the problem? The function f(x) = 10x represents total sales of tickets on opening night of a play. 3. Write and solve an inequality that represents how many tickets would need to be sold to earn total sales of more than $850. The function f(x) = 10x represents total sales of tickets on opening night of a play. 4. Solve f(x) < 900. What does this mean in the context of the problem? #1 x 60 #2 x 75; They would need to sell 75 tickets or more to earn at least $1250 #3 x > 35 #4 x < 40; They would need to sell less than 40 tickets to earn less than $900

8 5(2x + 3) + 2x = 12 10x x = 12 10x + 2x + 15 = 12 12x = x = 3 12x 12 = 3 12 x = x x = 12x x x = 12x + 2 5x + 4x + 4 = 12x + 2 9x = 12x x = 12x 2 9x 12x = 12x 12x 2 3x = 2 3x 3 = 2 3 x = x = 3x 8 x + x = 3x + x 8 = 2x 8 2 = 2x 2 4 = x

9 5(2x + 3) + 2x = 12 10x x = 12 10x + 2x + 15 = 12 12x = x = 3 12x 12 = 3 12 x = 1 4 Distributive Property Commutative Property Subtraction Property of Equality Additive Identity Division Property of Equality Multiplicative Identity 15x x = 12x x x = 12x + 2 5x + 4x + 4 = 12x + 2 9x = 12x x = 12x 2 9x 12x = 12x 12x 2 3x = 2 3x 3 = 2 3 x = 2 3 Division/Simplification Commutative Property Subtraction Property of Equality Additive Identity Subtraction Property of Equality Additive Identity Division Property of Equality Multiplicative Identity 8 x = 3x 8 x + x = 3x + x 8 = 2x Addition Property of Equality Additive Identity 8 2 = 2x Division Property of Equality 2 4 = x Multiplicative Inverse