Document Sample

SOLVING ABSOLUTE-VALUE EQUATIONS You can solve some absolute-value equations using mental math. For instance, you learned that the equation | x | 8 has two solutions: 8 and 8. To solve absolute-value equations, you can use the fact that the expression inside the absolute value symbols can be either positive or negative. Solving an Absolute-Value Equation Solve | x 2 | 5 SOLUTION The expression x 2 can be equal to 5 or 5. x 2 IS POSITIVE x 2 IS POSITIVE || x 2 || 5 x2 5 x 2 5 x 2 5 x 2 IS NEGATIVE |x2|5 x 2 5 x 3 x7 x7 The equation has two solutions: 7 and –3. CHECK |72||5|5 | 3 2 | | 5 | 5 Solving an Absolute-Value Equation Solve | 2x 7 | 5 4 SOLUTION Isolate the absolute value expression on one side of the equation. 2x 7 IS POSITIVE IS POSITIVE 2x 7 IS NEGATIVE IS NEGATIVE | 2x 7 | 5 4 | 2x 7 | 9 2x 7 9 9 2x 2 TWO SOLUTIONS x 1 | 2x 7 | 5 4 | 2x 7 | 9 2x 7 +9 2x 16 x8 Solving an Absolute-Value Equation Recall that | xis the distance between xxand 0. IfIf xx x | is the distance between and 0. | | 8, 8, then any number between and 8 8 is a solution of the then any number between 88 andis a solution of the inequality. 8 7 6 5 4 3 2 1 8 0 1 2 3 4 5 6 7 You can use the following properties to solve absolute-value inequalities and equations. SOLVING ABSOLUTE-VALUE INEQUALITIES SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES | ax b | c means ax b c and a x b c. | a x b | an absolute value b less than a number, c. a x is c and a x b the When c means inequalities are connected by and. When an absolute | a x b | cgreater thana x number, the inequalities c. or a x b are value is means a bc connected by or. | ax b | c means means ax b c or a x b c. | ax b | c ax b c or a x b c. Solving an Absolute-Value Inequality Solve | x 4 | < 3 x 4 IS POSITIVE |x4|3 x 4 3 x7 x 4 IS NEGATIVE |x4|3 x 4 3 x1 Reverse inequality less than The solution is all real numbers greater than 1 and symbol. 7 This can be written as 1 x 7. Solving an Absolute-Value Inequality Solve | 2x 1 | 3 6 and graph the 2x + 1 IS POSITIVE 2x + 1 IS NEGATIVE solution. 2x + 1 IS POSITIVE 2x | 1 | 6 | 2x| 1 3 9 2x 1 9 | 2x 1 |+9 | 2x 1 | 3 6 2x + 1 IS NEGATIVE 2x | 1 | 9 | 2x| 1 3 6 | 2x 1 | 3 6 2x 1 9 | 2x 1 | 9 2x 10 2x 8 2x 1 9 2x 1 +9 x is x 5 The solution 4all real numbers greater10 or 2x than 2x 8 equal x4 x 5 to 4 or less than or equal to 5. This can be written as the compound inequality x 5 or x 4. Reverse 5 inequality symbol. 4. 6 5 4 3 2 1 0 1 2 3 4 5 6 Writing an Absolute-Value Inequality You work in the quality control department of a manufacturing company. The diameter of a drill bit must be between 0.62 and 0.63 inch. a. Write an absolute-value inequality to represent this requirement. b. Does a bit with a diameter of 0.623 inch meet the requirement? Writing an Absolute-Value Inequality The diameter of a drill bit must be between 0.62 and 0.63 inch. a. Write an absolute-value inequality to represent this requirement. Let d represent the diameter (in inches) of the drill bit. Write a compound inequality. Find the halfway point. Subtract 0.625 from 0.62 d 0.63 0.625 0.62 0.625 d 0.625 0.63 0.625 each part of the 0.005 d 0.625 0.005 compound inequality. an absolute-value inequality. d 0.625 | 0.005 Rewrite as | This inequality can be read as “the actual diameter must differ from 0.625 inch by no more than 0.005 inch.” Writing an Absolute-Value Inequality The diameter of a drill bit must be between 0.62 and 0.63 inch. b. Does a bit with a diameter of 0.623 meet the requirement? | d 0.625 | 0.005 | 0.623 0.625 | 0.005 | 0.002 | 0.005 0.002 0.005 Because 0.002 0.005, the bit does meet the requirement.

DOCUMENT INFO

Shared By:

Categories:

Stats:

views: | 121 |

posted: | 6/1/2008 |

language: | English |

pages: | 10 |

OTHER DOCS BY LisaB1982

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.