Equations, Inequalities, and Problem Solving|Mathematics
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 2 over 3 x space plus 7 over 2 equals space 3 the same as 4x + 21=18? What property was used to rewritex
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.
