# Inequalities, and Problem Solving Unit Project

**Unit 2: Equations, Inequalities, and Problem Solving Unit Project**

Solve each equation below and justify your steps using a proof table. Show your work.

1. 12x – 4(2x – 10) = 6 – (x + 3)

2. 3(x – 2) + 7 = -4 + 2(x + 1)

3. Why is the same as 4x + 21=18? What property was used to rewrite x

4. Fishing Adventures rents small fishing boats to tourists for daylong fishing trips. Each boat can only carry 1500 pounds of people and gear for safety reasons. Assume the average weight of a person is 150 pounds. Each group will require 200 lbs of gear for the boat plus 10 lbs of gear for each person.

a. Create an inequality describing the restrictions on the number of people possible in a rented boat. Solve the inequality, write your answer in interval notation, and graph the solution set.

b. Several groups of people wish to rent a boat. Group 1 has 4 people. Group 2 has 5 people. Group 3 has 8 people. Which of the groups, if any, can safely rent a boat? What is the maximum number of people that may rent a boat?

5. The table below gives recommended weight ranges for the balls from five different sports. (Hint: Find the average of each weight.)

**Sport**

**Weight range of ball used**

Volleyball

260-280 grams

Basketball

600-650 grams

Water Polo

400-450 grams

Lacrosse

142-149 grams

Football

14-15 ounces

a. Write an absolute value inequality for the weight range of each ball.

b. For each ball, write an absolute value inequality describing the weights of balls that are outside the recommended range.

STATEMENTS REASONS 4(x+1) – 2x = -6(x-1) + 14 Given 4x + 4 – 2x = -6x + 6 + 14 Distributive property 2x + 4 = -6x + 20 Combining like terms 8x + 4 = 20 Addition property of equality 8x = 16 Subtraction property of equality x = 2 Division property of equality

Question 1 Uses two column proof format 1 point Shows 6 correct statements including given 5 points Shows 6 correct reasons including given 5 points Total 11 points Question 2 Uses two column proof format 1 point Shows 5 correct statements including given 4 points Shows 5 correct reasons including given 4 points Total 9 points Question 3 Explains why equations are equal 1 point Identifies correct property of equality 1 point Total 2 points Question 4 Writes inequality for the problem 1 point Correct solution to inequality 1 point Inequality written in interval notation 1 point Correct graph of inequality 1 point Correct groups identified in part b 1 point Correct maximum number of people 1 point Total 6 points Question 5 Absolute value inequality written for each ball range 5 points Absolute value inequality written for excluded values for each ball 5 points Total 10 points