Equations and Inequalities

1. Chapter 2 Equations and Inequalities

2. Chapter Sections 2.1 – 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

3. Additional Application Problems § 2.4

4. Solve Motion Problems A motion problemis one in which an object is moving at a specified rate for a specified period of time. amount = rate · time Continued.

5. Distance Problems When the amount in the formula is distance, we refer to the formula as the distance formula. distance = rate · time or d = r · t Continued.

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. Distance Problems Example continued: distance = rate · time or d = r · t The difference between their distances is 105 miles. Thus, aircraft carrier’s distance – submarine’s distance = 105 34t - 20t = 105 14t = 105 t = 7.5 The aircraft carrier and submarine will be 105 miles apart in 7.5 hours.

8. Mixture Problems 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. strength · quantity = amount

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. Mixture Problems Example continued: Let x = number of mL of 10% tea tree oil solution Solve the equation. Continued.

11. Mixture Problems Example continued: Amount of tea tree oil 3% solution Amount of tea tree oil 3% solution Amount of tea tree oil 3% solution + = 0.03(5) + 0.10(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 5 + 2 = 7 mL of the 5% solution.