of 36 /36
Section 4.4 Solving Absolute Value Equations and Inequalities

# Section 4.4 Solving Absolute Value Equations and Inequalities

Embed Size (px)

### Text of Section 4.4 Solving Absolute Value Equations and Inequalities

• Slide 1
• Section 4.4 Solving Absolute Value Equations and Inequalities
• Slide 2
• 4.4 Lecture Guide: Solving Absolute Value Equations and Inequalities Objective 1: Use absolute value notation to represent intervals.
• Slide 3
• AlgebraicallyVerbally The distance from 0 to x is d units. The distance from 0 to x is __________ than d units. The distance from 0 to x is __________ than d units. Numerical Example Graphical Example if or if and if or 33 3 0 ( ) 33 3 0 ( ) 33 3 0 Absolute Value Expressions For any real number x and any nonnegative real number d:
• Slide 4
• Use interval notation to represent the real numbers that are solutions of these inequalities. 1.2.
• Slide 5
• Write an absolute-value inequality to represent each set of points. 3. 4.
• Slide 6
• Write an absolute-value inequality to represent each set of points. 5. The points between 6 and 6. 6. 22044668810246810
• Slide 7
• Use absolute value to represent the distance between these real numbers. 7. 8. 9. y and x x and 10 x and
• Slide 8
• 10. Write an absolute value equation indicating that the distance from to a isunits.
• Slide 9
• Objective 2: Solve absolute value equations and inequalities.
• Slide 10
• AlgebraicallyVerbally x is either d units _________ or __________ of a. x is _________ than d units from a. Equivalent Expressions Graphically a da + d a ( ) a ( ) a Solving Absolute Value Equations and Inequalities For any real number x and any nonnegative real number d: a da + d a da + d
• Slide 11
• Similar statements can also be made about the order relations less than or equal to and greater than or equal to Expressions with d negative are examined in the group exercises at the end of this section.
• Slide 12
• Write an absolute-value inequality to represent each interval. First graph the interval and use this graph to assist you in writing the inequality. 11.
• Slide 13
• Write an absolute-value inequality to represent each interval. First graph the interval and use this graph to assist you in writing the inequality. 12.
• Slide 14
• Solve each equation or inequality algebraically. 13.
• Slide 15
• Solve each equation or inequality algebraically. 14.
• Slide 16
• Solve each equation or inequality algebraically. 15.
• Slide 17
• Solve each equation or inequality algebraically. 16.
• Slide 18
• Solve each equation or inequality algebraically. 17.
• Slide 19
• Solve each equation or inequality algebraically. 18.
• Slide 20
• Solve each equation or inequality algebraically. 19.
• Slide 21
• Solve each equation or inequality algebraically. 20.
• Slide 22
• If, then a and b are equal in magnitude but their signs can either agree or disagree. Thus is equivalent to ______________ or ______________. Use this result to solve the next two problems.
• Slide 23
• 21. Solve.
• Slide 24
• 22. Solve.
• Slide 25
• 23. Use the graph to solve each equation or inequality. (a) (b) (c)
• Slide 26
• 24. Use the table to solve each equation or inequality. (a) (b) (c)
• Slide 27
• Solve each equation or inequality algebraically. Use the given graph to solve each equation or inequality graphically. Then complete the table to check your solutions numerically. 25.
• Slide 28
• Solve each equation or inequality algebraically. Use the given graph to solve each equation or inequality graphically. Then complete the table to check your solutions numerically. 26.
• Slide 29
• Solve each equation or inequality algebraically. Use the given graph to solve each equation or inequality graphically. Then complete the table to check your solutions numerically. 27.
• Slide 30
• Solve each equation or inequality algebraically. Use the given graph to solve each equation or inequality graphically. Then complete the table to check your solutions numerically. 28.
• Slide 31
• Solve each equation or inequality algebraically. Use the given graph to solve each equation or inequality graphically. Then complete the table to check your solutions numerically. 29.
• Slide 32
• Solve each equation or inequality algebraically. Use the given graph to solve each equation or inequality graphically. Then complete the table to check your solutions numerically. 30.
• Slide 33
• Write an absolute value inequality to represent the following intervals. Hint: First sketch a graph of these inequalities. 31. 32.
• Slide 34
• Write an absolute value inequality to represent the following intervals. Hint: First sketch a graph of these inequalities. 33.34.
• Slide 35
• 35. The correct torque setting for the lug bolts on a race car is 85 foot-pounds with a tolerance of 3 foot-pounds. (a) Express the acceptable torque setting as an absolute value inequality. (b) Express the acceptable torque setting as a compound linear inequality.
• Slide 36
• 35. The correct torque setting for the lug bolts on a race car is 85 foot-pounds with a tolerance of 3 foot-pounds. (c) Determine the lower and upper limits of the interval. ##### Absolute Value Equations and Inequalities · ABSOLUTE VALUE EQUATIONS AND INEQUALITIES B. ABSOLUTE VALUE INEQUALITIES: O When solving inequalities of the form O , we need to find
Documents ##### Inequalities: Linear and Absolute Value; Classnotes Linear and Absolute Value; Classnotes ... 1.7 Inequalities: Linear and Absolute Value Class Notes: Prof. G. Battaly, Westchester
Documents ##### Absolute value inequalities - Integers - Free Math WorksheetsSolve an inequality and graph the solution of inequalities with two operations: 501) b ... Absolute value inequalities
Documents ##### Pre-Calculus Lesson 7: Solving Inequalities Linear inequalities, compound inequalities, absolute value inequalities, interval notation
Documents ##### Situation 47: Graphing Inequalities with Absolute Valuesjwilson.coe.uga.edu/.../Situation.47/060510_SituationAbsGraph.pdf · Situation 47: Graphing Inequalities with Absolute
Documents ##### Chapter 2.7 – Absolute Value Inequalities. Objectives Solve absolute value inequalities of the form /x/ < a Solve absolute value inequalities of the form
Documents ##### Section 1.7 Linear Inequalities and Absolute Value Inequalities
Documents ##### Absolute Value Equations and Inequalities · Section 4.3 Absolute Value Equations and Inequalities Page 5 . Section 4.3 Absolute Value Equations and Inequalities Page 6 . Created
Documents ##### 9.20 Absolute Value Equations and Inequalities Notes · 9.20 Absolute Value Equations and Inequalities Notes 4 September 20, 2013 Sections 6.5 6.6 Absolute Value Equations and Inequalities
Documents ##### ABSOLUTE VALUE EQUATIONS AND INEQUALITIES...2018/05/01  · ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 09 Solving an absolute value inequality problem is similar to solving an absolute
Documents ##### 1 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Absolute-Value Equations and Inequalities Equations with Absolute Value Inequalities with Absolute
Documents ##### P.9 Linear Inequalities and Absolute Value Inequalities Notessevillaj.weebly.com/uploads/7/7/8/4/7784014/p.9... · Linear Inequalities and Absolute Value Inequalities 2 B Because
Documents ##### 5.6 Solve Absolute Value Inequalities You will solve absolute value inequalities. Essential question: How do you solve absolute value inequalities? You
Documents ##### 2.6 Absolute Value. Goals SWBAT solve inequalities involving absolute value
Documents ##### Goal: Solve absolute value inequalities. Eligible Content: A1.1.1.3.1 / A1.1.3.1.1 / A1.1.3.1.2 / A1.1.3.1.3 5-5 Absolute Value Inequalities
Documents ##### NOTES: Absolute Value Equations and Inequalities · 9/9/2012  · NOTES: Absolute Value Equations and Inequalities Define absolute value (geometrically):_----'dc:.t= ... an absolute
Documents ##### Chapter 4: Solving Inequalities 4.6 Absolute Value Equations and Inequalities
Documents ##### Absolute Value Equations and Inequalities - Cypress Collegenews.cypresscollege.edu/Documents/sem/Absolute...Absolute Value Equations and Inequalities Objective 1: Solving Absolute
Documents Documents