Directed Distance & Absolute Value Objective: To be able to find directed distances and solve absolute value inequalities. TS: Making Decisions after Reflection.

Slides:

Advertisements

Similar presentations

Special Equations - Absolute Value and Interval Notation

Advertisements

A.6 Linear Inequalities in One Variable Interval Not.Inequality Not.Graph [a,b] (a,b) [a,b) (a,b] [ ] a b.

Appendix B.4 Solving Inequalities Algebraically And Graphically.

LIAL HORNSBY SCHNEIDER

Ch 2.2 Objective: To solve problems involving absolute value of numbers or variables.

2.6 Equations and Inequalities Involving Absolute Value BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 By looking at the equation, what number.

Solving Absolute Value Equations and Inequalities.

ABSOLUTE VALUE EQUALITIES and INEQUALITIES

Calculus X Solving Inequalities Algebraically Unit 1 TS: Making Decisions After Reflection & Review Objective: Be able to solve inequalities algebraically.

1.8 Solving Absolute Value Equations and Inequalities

Absolute Value Inequality

Absolute Value Equalities and Inequalities Absolute value: The distance from zero on the number line. Example: The absolute value of 7, written as |7|,

Directed Distance & Absolute Value Objective: To be able to find directed distances and solve absolute value inequalities. TS: Making Decisions after Reflection.

Warm Up Solve. 1. y + 7 < – m ≥ – – 2x ≤ 17 y < –18 m ≥ –3 x ≥ –6 Use interval notation to indicate the graphed numbers (-2, 3] (-

Algebra II w/ trig. Compound inequality: two inequalities joined by “and” or “or” AND graph means both inequalities are true (think: between, alike) OR.

Chapter 2.7 – Absolute Value Inequalities. Objectives Solve absolute value inequalities of the form /x/ < a Solve absolute value inequalities of the form.

4-6 Solving Absolute Value Equations & Inequalities

Solve Absolute Value Inequalities © 2011 The Enlightened Elephant.

Lesson 5 Contents Glencoe McGraw-Hill Mathematics Algebra 2005 Example 1Solve an Absolute Value Equation Example 2Write an Absolute Value Equation.

3.6 Solving Absolute Value Equations and Inequalities

How can we express Inequalities?

You walk directly east from your house one block. How far from your house are you? 1 block You walk directly west from your house one block. How far from.

Warm-Up Solve the following Inequalities:

Solving Absolute Value Equations & Inequalities Solving Absolute Value Equations & Inequalities Isolate the absolute value.

6.5 Solving Inequalities by Factoring. Steps to Solve To solve an inequality by factoring, treat the inequality like an sign and solve. Make sure to set.

Goal: Solve and write absolute value equations in one variable Section 4-4: Solving Absolute Value Equations.

Solving Open Sentences Involving Absolute Value

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

Absolute Value Equations Inequalities. What is Absolute Value?  The distance away from the origin (zero) on a number line.  Distances cannot be negative.

October 31, 2012 Solving Absolute Value Inequalities DO NOW: Solve │x + 13│ = 8 3. │3x – 9│= -24 HW 6.5b: Pg. 350 #29- 39, skip 36 and 38 Unit Test.

Solving Absolute Value Equations & Inequalities Solving Absolute Value Equations & Inequalities Zafar-iqbal.

ABSOLUTE VALUE INEQUALITIES.  Just like absolute value equations, inequalities will have two solutions: |3x - 2| ≤ 7 3x – 2 ≤ x ≤ 9 x ≤ 3 -5/3.

Objective SWBAT solve absolute value equations.. ABSOLUTE VALUE –The distance a number is away from ZERO. Distance is always positive

HOMEWORK REVIEW. SOLVE ABSOLUTE VALUE INEQUALITIES 5.5.

1.7 “Absolute Value” Absolute Value is always positive!! 7 = 7-7 = 7 **When solving equations or inequalities, you MUST set up 2 separate problems, one.

1.8 Solving Absolute Value Equations and Inequalities Objectives: Write, solve, and graph absolute value equations and inequalities in mathematical and.

2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value.

1.7 Solving Absolute Value Equations and Inequalities ©2001 by R. Villar All Rights Reserved.

Lesson 1.4 Equations and Inequalities Goal: To learn how to solve equations and check solutions of equations and inequalities.

Algebra Review: Solving Quadratic Equations by Factoring.

1-4 Solving Absolute Value Equations Objectives Students will be able to: 1)Evaluate expressions involving absolute values 2)Solve absolute value equations.

Linear Inequalities in One Variable Objective: To solve linear inequalities.

Section 3-1 Linear Inequalities; Absolute Value. Inequalities Inequalities can be written in one or more variables. Linear Inequalities: 2x + 3y > 6 Polynomial.

Chapter 1.8 Absolute Value and Inequalities. Recall from Chapter R that the absolute value of a number a, written |a|, gives the distance from a to 0.

Absolute Value Absolute Value is the distance a number is away from zero on the number line. Find.| 4 | 4 | – 4 | 4 * Absolute Value Is ALWAYS POSITIVE!!!!*

Chapter 8 Unit Question How do inequalities affect algebraic concepts?

Algebra Solving Absolute Value Equations and Inequalities.

CHAPTER 1 – EQUATIONS AND INEQUALITIES 1.4 – SOLVING ABSOLUTE VALUE EQUATIONS Unit 1 – First-Degree Equations and Inequalities.

What is the difference between > and

Note #6 Standard: Solving Absolute-Value Equation and Inequalities Objective - To solve an equation involving absolute value.

Absolute Value Equations and Inequalities

Solving Graphically Ex 1: View using the following windows.

Chapter 2 Section 2 Absolute Value

1.6 Absolute Value Learning Goals

3.3 – Solving Systems of Inequalities by Graphing

Warm-up Solve each equation 4+13= −3+7= 4−13= −3−7=

2.4 & 2.5 Absolute Value Inequalities and Equations

Equations and Inequalities involving Absolute Value

Drill Write the compound inequality for the following graphs.

Pre- Calculus Lesson 1.1 begin Chapter 1: Functions.

Solving Equations with Variables on Both Sides Day 2

6.5 Solving Inequalities by Factoring

Objectives Solve equations that contain absolute-value expressions.

Absolute Value Inequalities

1.6 Solving Linear Inequalities

Solve multi step equations and inequalities.

Solving Equations with Variables on Both Sides Day 2

1-6: Absolute Value Equations

Presentation transcript:

Directed Distance & Absolute Value Objective: To be able to find directed distances and solve absolute value inequalities. TS: Making Decisions after Reflection and Review Warm Up: Solve the following absolute value equation. |2x – 3| = 13

Distance Between Two Points. What is the distance between the two values of 10 and 2? What is the distance between the two values of -102 and 80? So the distance between two points x 1 and x 2 is |x 1 – x 2 | or |x 2 – x 1 | 8 182

Directed Distance The directed distance from a to b is b – a. Ex: Find the directed distance from 5 to – The directed distance from b to a is a – b. Ex: Find the directed distance from -10 to 5 5 – (-10) 15

Midpoint The midpoint between to values is a + b 2 Ex: Find the midpoint of the interval [1, 10]

Absolute Value Not true Is this statement true?

Absolute Value Think of absolute value as measuring a distance.

Absolute Value Absolute Value: The distance a number is from zero on a number line. It is always positive or zero.

Absolute Value ( ) The < sign indicates that the value is center around 0 and no more than 3 away.

Absolute Value ( ) The < sign indicates that the value is center around 2 and no more than 3 away. NOTICE: 2 is the midpoint of -1 and 5.

Absolute Value ] [ The > sign indicates that the value is diverging from points on either side of 0.

Absolute Value ] [ The > sign indicates that the value is diverging from points on either side of -3. NOTICE: -3 is the midpoint of -4 and -1.

Writing an Absolute Value 1)Write an absolute value inequality for the below intervals: (-∞, - 4]U[4, ∞) (-5, 5) (- ∞, 2)U(5, ∞) [-10, 20]

Absolute Value What does this statement mean? ( )

Absolute Value ] [ What does this statement mean?

Absolute Value

You Try Solve the following inequalities: 1) |2x|< 6 2) |3x+1|≥4 3) |25 – x|>20 Ans: (-3, 3) Ans: (-∞,-5/3] U [1,∞) Ans: (-∞,5) U (45,∞)

Conclusion Absolute value is the distance a number is from zero on a number line. Two equations are necessary to solve an absolute value equation. Two inequalities are necessary to solve an absolute value inequality.