1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Equations and Inequalities Chapter 2

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Solving Linear Equations 2.2 – Problem Solving and Using Formulas 2.3 – Applications of Algebra 2.4 – Additional Application Problems 2.5 – Solving Linear Inequalities 2.6 – Solving Equations and Inequalities Containing Absolute Values Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3 § 2.4 Additional Application Problems

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4 Solve Motion Problems A motion problem is one in which an object is moving at a specified rate for a specified period of time. amount = rate · time Continued.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5 Distance Problems distance = rate · time or d = r · t When the amount in the formula is distance, we refer to the formula as the distance formula. Continued.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6 Solve Distance Problems The aircraft carrier USS John F. Kennedy and the nuclear powered submarine USS Memphis leave from the Puget Sound Naval Yard at the same time heading for the same destination in the Indian Ocean. The aircraft carrier travels at 34 miles per hour and the submarine travels at 20 miles per hour. The aircraft carrier and submarine are to travel at these speeds until they are 105 miles apart. How long will it take for the aircraft carrier and submarine to be 105 miles apart?

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7 Distance Problems The difference between their distances is 105 miles. Thus, aircraft carrier’s distance – submarine’s distance = t - 20t = t = 105 t = 7.5 The aircraft carrier and submarine will be 105 miles apart in 7.5 hours. distance = rate · time or d = r · t Example continued: RateTimeDistance Aircraft Carrier34t34t Submarine20t20t

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-8 Mixture Problems strength · quantity = amount Any problem where two or more quantities are combined to produce a different quantity or where a single quantity is separated into two or more different quantities may be considered a mixture problem.

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-9 Mixture Problems Example: Christine Fogal, an herbalist, needs a 5% tea tree oil solutions to use as a topical treatment for skin rash caused by poison ivy. Christine only has tea tree oil solutions that have concentrations of 3% and 10%, respectively. How many milliliters (mL) of the 10% tea tree oil solutions should Christine mix with 5 mL of the 3% tea tree oil solution to create the desired 5% tea tree oil solution? Continued.

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-10 Mixture Problems SolutionStrength of Solution Volume of Solution (number of mL) Amount of Tea Tree Oil (5) x0.10(x) Mixture x0.05(5 + x) Let x = number of mL of 10% tea tree oil solution Solve the equation. Example continued: Continued.

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-11 Mixture Problems 0.03(5) (x) = 0.05(5 + x) Check: Christine must mix 2 mL of the 10% tea tree oil solution with the 5 mL of the 3% tea tree oil solution to make 5% tea tree oil solution. There will be 5 + x or = 7 mL of the 5% solution. Example continued: Amount of tea tree oil 3% solution + =