1. College Algebra Chapter 1 Equations and Inequalities
Section 1.6
More Equations and Applications
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2. Concepts Solve Polynomial Equations Solve Rational Equations
Solve Absolute Value Equations
Solve Radical Equations and Equations with Rational Exponents
Solve Equations in Quadratic Form

3. Concept 1 Solve Polynomial Equations

4. Example 1
Solve

5. Skill Practice 1
Solve the equation.

6. Example 2
Solve

7. Skill Practice 2
Solve the equation.

8. Concept 2 Solve Rational Equations

9. Example 3
Solve

10. Example 4
Solve

11. Skill Practice 3
Solve

12. Skill Practice 4
A fishing boat can travel 60 km with a 2.5-km/hr current in 2 hour less time than it can travel 60 km against the current. Determine the speed of the fishing boat in still water.

13. Concept 3 Solve Absolute Value Equations

14. Solve Absolute Value Equations
If k > 0, then |u| = k is equivalent to u = k or u = -k. Example: |x| = 4
If k < 0, then |u| = k has no solutions If k = 0, then |u| = k is equivalent to u = 0 |u| = |w| is equivalent to u = w or u = -w

15. Example 5
Solve |2x – 1| = 5

16. Example 6
Solve 2|x – 4| + 1 = 7

17. Example 7
Solve |x + 2| = -3

18. Example 8
Solve |x + 2| = 0

19. Skill Practice 5
Solve the equations.
5|2 - 4t| = 50
5 = |6c – 7| + 9

20. Example 9
Solve |3x – 1| = |x + 5|

21. Skill Practice 6 Solve the equation |3x – 4| = |2x + 1|

22. Concept 4 Solve Radical Equations and Equations with Rational Exponents

23. Solving a Radical Equation (1 of 2)
Step 1: Isolate the radical. If an equation has more than one radical, choose one of the radicals to isolate. Step 2: Raise each side of the equation to a power equal to the index of the radical. Step 3: Solve the resulting equation. If the equation still has a radical, repeat steps 1 and 2. Step 4: Check the potential solutions in the original equation and write the solution set.

24. Solving a Radical Equation (2 of 2)
In solving radical equations, extraneous solutions potentially arise when both sides of the equation are raised to an even power. Therefore, an equation with only odd-indexed roots will not have extraneous solutions. However, it is still recommended that all potential solutions be checked.

25. Example 10
Solve

26. Skill Practice 7
Solve the equation.

27. Example 11
Solve

28. Skill Practice 8
Solve.

29. Example 12
Solve

30. Example 13
Solve

31. Skill Practice 9
Solve the equation.

32. Concept 5 Solve Equations in Quadratic Form

33. Example 14
Solve

34. Example 15
Solve

35. Example 16
Solve

36. Example 17
Solve

37. Example 18
Solve

38. Skill Practice 10
Solve.

39. Skill Practice 11
Solve

40. Concepts Mixed Exercises

41. Example 19
Solve for x

42. Example 20
Solve for a

43. Example 21
Reynaldo is on the beach playing catch with his dog, Rex Ruthor. When Reynaldo tosses the ball into the water, Rex races down the shore, then dives into the water and swims to the ball. Rex can run 10 feet per second and swim 2 feet per second. Reynaldo tosses the ball into the water so that it lands 6 feet from the shore and 38 feet along the shoreline. If it takes Rex a total of 8 seconds to get to the ball, how far along the shore did he run before diving in?

44. Example 22 (1 of 2)
Kleiber's law gives a relationship between an animal's metabolic rate, MR, and its body mass, m.
where MR is measured in kilocalories per day and m is weight in kilograms.
Find the metabolic rate of a lab mouse weighing 0.02 kilograms (about twice the mass of a pencil). Round to the nearest whole unit.

45. Example 22 (2 of 2)
Find the metabolic rate of an African elephant weighing 3000 kilograms (about 1 Ford Taurus). Round to the nearest whole unit.
What is the mass of a house cat that has a metabolic rate of 245 kilocalories per day? Round your answer to the nearest unit.