# Absolute Value Equations and Inequalities · PDF file ABSOLUTE VALUE EQUATIONS AND INEQUALITIES B. ABSOLUTE VALUE INEQUALITIES: O When solving inequalities of the form O , we need

• View
5

0

Embed Size (px)

### Text of Absolute Value Equations and Inequalities · PDF file ABSOLUTE VALUE EQUATIONS AND...

• Absolute Value Equations and  Inequalities Unit 3 Lesson 7

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Students will be able to: solve absolute value equations and inequalities.

Key Vocabulary:  Absolute Value Equations  Absolute Value Inequalities

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

The three types of open sentences that can involve absolute value:

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

A.  ABSOLUTE VALUE EQUATIONS:  When solving equations involving absolute value, we need to  consider these cases

a.  The value inside the absolute value symbols is positive.

b.  The value inside the absolute value symbols is negative.

If , then  or  .

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. A. | |

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. A. | |

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. A. | |

Check:

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. B.

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. B. /

/

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. B. / Check: //

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. C.

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. C.

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 1: Solve each equation and graph the solution set. C. Check:

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

B. ABSOLUTE VALUE INEQUALITIES:  When solving inequalities of the form , we need to find the  Intersection of these cases:

a.  The value inside the absolute value symbols is less than the  positive value of .  b.  The value inside the absolute value symbols is greater than  the negative value of .

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

B. ABSOLUTE VALUE INEQUALITIES:  If  , then  and  .

It also applies for  :  If  , then  and  .

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. A.

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. A.

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. A.

Check:

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. A.

Check:

≮ ≮

0 1 2 3 4-1-2 5 6 7 8 9

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. B.

0 2 4 6 8-2-4-6-8 10-14 -10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. B. /

/

0 2 4 6 8-2-4-6-8 10-14 -10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. B. / Check: / //

0 2 4 6 8-2-4-6-8 10-14 -10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. B. / Check:

0 2 4 6 8-2-4-6-8 10-14 -10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. C.

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. C.

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. C.

Check:

≮ ≮

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 2: Solve each equation and graph the solution set. C.

Check:

≮ ≮

0 2 4 6 8-2-4-6-8 10 12-10-12

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

C. ABSOLUTE VALUE INEQUALITIES:  When solving inequalities of the form , we need to find the  Intersection of these cases:

a. The value inside the absolute value symbols is GREATER THAN  THE POSITIVE VALUE OF .  b. The value inside the absolute value symbols is LESS THAN THE  NEGATIVE VALUE OF .

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

C. ABSOLUTE VALUE INEQUALITIES:  If  , then  or  .

It also applies for :  If  , then  or  .

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. A.

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. A. or

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. A.    or

Check:

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. A.    or

Check:

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. B.

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. B.

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. B. Check:

≯ ≯

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. B. Check:

≯ ≯

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. C.

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. C.

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. C. Check:

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 3: Solve each equation and graph the solution set. C. Check:

0 4 8 12 16-4-8-12-16 20 24-20-24

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 4: The starting players of the school’s varsity  basketball team have an average scoring point between 9 and 20.  Write an absolute value inequality describing the average scoring  point of the starting players.

Step 1 Write the inequality.

Step 2 Determine the midpoint.

Step 3 Determine the distance from the midpoint.

Step 4 Write the absolute value inequality. (Use appropriate inequality symbol)

• ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Sample Problem 4: The starting players of the school’s varsity  basketball team have an average scoring point between 9 and 20.  Write an absolute value inequality describing the average scoring  point of the starting players.

Step 1 Write the inequality.

Step 2 Determine the midpoint. . Step ##### 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 ##### 5.6 Solve Absolute Value Inequalities You will solve absolute value inequalities. Essential question: How do you solve absolute value inequalities? You
Documents ##### Section 1.7 Linear Inequalities and Absolute Value Inequalities
Documents ##### SOLVING TWO VARIABLE LINEAR INEQUALITIES INCLUDING ABSOLUTE VALUE INEQUALITIES
Documents ##### Absolute Value Equations and Inequalities - Cypress ... Absolute Value Equations and Inequalities Objective
Documents ##### Solving Absolute Value Inequalities - 2018-10-13آ  Solving Absolute Value Inequalities 3 EXAMPLE 3 Real-Life
Documents ##### 19-21 Absolute Value Inequalities Real World ... 2014/04/14 آ  19 21 Absolute Value Inequalities Real
Documents ##### ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 2018-01-30آ  ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 09
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 ##### 3-7 Absolute Value Equations and Inequalities 3-7 Absolute Value Equations and Inequalities Write T
Documents ##### MAT01A1 0.5cm Numbers, Inequalities and Absolute Values ... ... Solving absolute value inequalities:
Documents ##### Title: Teaching absolute value inequalities to mature ... absolute value and absolute value inequalities
Documents ##### Section Linear Inequalities and Absolute Objectives Value ... Section P.9 Linear Inequalities and Absolute
Documents ##### CollegeAlgebra 04 Equations and Inequalities ... Absolute Value Equations An absolute value equationin
Documents Documents