Solving an Absolute-Value Inequality Recall that  x  is the distance between x and 0. If  x  8, then any number between  8 and 8 is a solution of.

Slides:

Advertisements

Similar presentations

Name: Date: Period: Topic: Solving Absolute Value Equations & Inequalities Essential Question: What is the process needed to solve absolute value equations.

Advertisements

Solve an absolute value inequality

Recall that the absolute value of a number x, written |x|, is the distance from x to zero on the number line. Because absolute value represents distance.

3-6 Compound Inequalities

I can solve and graph inequalities containing the words and and or. 3.6 Compound Inequalities.

1 Sections 17.1, 17.2, & 17.4 Linear and Absolute Value Inequalities.

EXAMPLE 1 Solve absolute value inequalities

Algebra 1 Chapter 3 Section 7.

Solve a compound inequality with and

1 Sections 17.1, 17.2, & 17.4 Linear and Absolute Value Inequalities.

Outcomes: Represent the solution sets to inequalities in the following formats: Graphically Symbolically With Words.

2-8 Solving Absolute-Value Equations and Inequalities Warm Up

Notes Over 6.3 Writing Compound Inequalities Write an inequality that represents the statement and graph the inequality. l l l l l l l

5.4 – Solving Compound Inequalities. Ex. Solve and graph the solution.

Set Operations and Compound Inequalities. 1. Use A = {2, 3, 4, 5, 6}, B = {1, 3, 5, 7, 9}, and C = {2, 4, 6, 8} to find each set.

Objectives Solve compound inequalities.

Chapter 2.5 – Compound Inequalities

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 6.6 Linear Inequalities.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Solving Absolute Value Equations and Inequalities

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. S OLVING.

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] (-

Compound Inequalities

4.1 Solving Linear Inequalities

Absolute Value Inequalities Algebra. Farmer Bob has four sheep. One day, he notices that they are standing in such a way that they are all the same distance.

A disjunction is a compound statement that uses the word or.

6-6 Solving Inequalities Involving Absolute Value Algebra 1 Glencoe McGraw-HillLinda Stamper.

1 – 7 Solving Absolute Value Equations and Inequalities Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.

How can we express Inequalities?

5.5 Solving Absolute Value Inequalities

Copyright © Cengage Learning. All rights reserved. Fundamentals.

6.4 Solving Absolute Value Equations and Inequalities

SOLVE ABSOLUTE VALUE INEQUALITIES January 21, 2014 Pages

Success Criteria:  I can interpret complicated expressions by viewing one or more of their parts as a single entity  Be able to create equations and.

Chapter 1 Section 1.7. Yesterday’s Exit Slip -2 Objectives: O To solve compound inequalities using and and or. O To solve inequalities involving absolute.

Chapter 2 Inequalities. Lesson 2-1 Graphing and Writing Inequalities INEQUALITY – a statement that two quantities are not equal. SOLUTION OF AN INEQUALITY.

Holt Algebra Solving Absolute-Value Equations and Inequalities Solve compound inequalities. Write and solve absolute-value equations and inequalities.

Solve an inequality using multiplication EXAMPLE 2 < 7< 7 x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > –42.

Do Now Solve and graph. – 2k – 2 < – 12 and 3k – 3 ≤ 21.

1.4 Solving Inequalities I can: 1.Graph inequalities 2.Solve inequalities.

Holt McDougal Algebra Solving Absolute-Value Inequalities Solve compound inequalities in one variable involving absolute-value expressions. Objectives.

Chapter 12 Section 5 Solving Compound Inequalities.

EXAMPLE 1 Graph simple inequalities a. Graph x < 2.

Notes Over 1.6 Solving an Inequality with a Variable on One Side Solve the inequality. Then graph your solution. l l l

Algebra 2 Lesson 1-6 Part 2 Absolute Value Inequalities.

1.7 Solving Absolute Value Inequalities. Review of the Steps to Solve a Compound Inequality: ● Example: ● You must solve each part of the inequality.

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

– 8 and 8 is a solution of the

Quiz Chapter 2 Ext. – Absolute Value

Ch 6.5 Solving Compound Inequalities Involving “OR”

Solving Absolute-Value Inequalities

2.6 Solving Absolute-Value Inequalities

Absolute Value Inequalities

Section 6.6 Linear Inequalities

1.7 Solving Absolute Value Inequalities

3-2 Solving Inequalities Using Addition or Subtraction

1.6 Solve Linear Inequalities

SOLVING ABSOLUTE-VALUE EQUATIONS

What is the difference between and and or?

Solve Absolute Value Inequalities

Sec 4-4B Solve Inequalities by addition and Subtraction

Absolute Value Inequalities

Absolute Value Inequalities

Notes Over 1.7 Solving Inequalities

Solve an inequality using subtraction

Notes Over 1.7 Solving Inequalities

SOLVING ABSOLUTE-VALUE EQUATIONS

Solving and Graphing Linear Inequalities

SOLVING ABSOLUTE-VALUE EQUATIONS

Presentation transcript:

Solving an Absolute-Value Inequality Recall that  x  is the distance between x and 0. If  x  8, then any number between  8 and 8 is a solution of the inequality.  8  7  6  5  4  3  2  Recall that | x | is the distance between x and 0. If | x |  8, then any number between  8 and 8 is a solution of the inequality.

Solve | x  4 | < 3 Solving an Absolute-Value Inequality x  4 IS POSITIVE x  4 IS NEGATIVE | x  4 |  3 x  4   3 x  7 | x  4 |  3 x  4   3 x  1 Reverse inequality symbol.  This can be written as 1  x  7. The solution is all real numbers greater than 1 and less than 7.

2x  1   9 | 2x  1 |  3  6 | 2x  1 |  9 2x   10 2x + 1 IS NEGATIVE  x   5 Solve | 2x  1 |  3  6 and graph the solution. | 2x  1 |  3  6 | 2x  1 |  9 2x  1  +9 2x  8 2x + 1 IS POSITIVE x  4 Solving an Absolute-Value Inequality Reverse inequality symbol. | 2x  1 |  3  6 | 2x  1 |  9 2x  1  +9 x  4 2x  8 | 2x  1 |  3  6 | 2x  1 |  9 2x  1   9 2x   10 x   5 2x + 1 IS POSITIVE 2x + 1 IS NEGATIVE  6  5  4  3  2  The solution is all real numbers greater than or equal to 4 or less than or equal to  5. This can be written as the compound inequality x   5 or x  4.  5

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. Write an absolute-value inequality to represent this requirement. a. Does a bit with a diameter of inch meet the requirement? b.

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  d  0.63 Find the halfway point Subtract from each part of the compound inequality   d   0.63    d   Rewrite as an absolute-value inequality. | d  |  This inequality can be read as “the actual diameter must differ from inch by no more than inch.”

The diameter of a drill bit must be between 0.62 and 0.63 inch. b. Does a bit with a diameter of meet the requirement? Writing an Absolute-Value Inequality | d  |  |  |  |  |  Because  0.005, the bit does meet the requirement  0.005