Mastering Absolute Value Equations and Inequalities: A Comprehensive Guide

Feb 08, 2026

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Unlock the secrets of absolute value equations and inequalities with our detailed guide. This resource offers clear explanations, step-by-step solutions, and practical examples to help you grasp the concepts effectively. Learn to solve such equations and inequalities, understand their graphs, and apply them to real-world scenarios. Perfect for students and anyone looking to improve their mathematical skills, this guide makes complex topics simple and accessible. Start mastering absolute value today!

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Mastering Absolute Value Equations and Inequalities: A Comprehensive Guide

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1.6 Absolute-Value Equations & Inequalities

1.6 Absolute-Value Equations & Inequalities. Absolute value of a number is its distance from zero on the number line. Absolute value of a number is never negative. If x ≥ 0, then |x| = x If x < 0, then |x| = -x. Properties of Absolute Value. For any real number a and b |ab| = |a| |b|

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2.2 Solve Absolute Value Equations and Inequalities

2.2 Solve Absolute Value Equations and Inequalities. Math Midterm: March 11. Vocabulary. Extraneous Solution An apparent solution that must be rejected because it does not satisfy the original equation. a FAKE solution. Example 1:. Solve |x – 3| = 6 .

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9.2 Absolute Value Equations and Inequalities

9.2 Absolute Value Equations and Inequalities. Use the distance definition of absolute value. Objective 1 . Slide 9.2- 2. The absolute value of a number x , written | x |, is the distance from x to 0 on the number line.

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Solve absolute Value Inequalities

Solve absolute Value Inequalities. Isolate the absolute value on one side of the equation. Write the problem as a compound inequality. LESS THAN: If absolute value is <a, then write the problem as a compound inequality -a< || < a GREATER THAN:

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Absolute Value Equations and Inequalities

2.5. Absolute Value Equations and Inequalities. Evaluate and graph the absolute value function Solve absolute value equations Solve absolute value inequalities. Definition of the Absolute Value Function. The graph of y = | x |. V-shaped Cannot be represented by single linear function.

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Solve absolute value equations

Solve absolute value equations. Section 6.5. Concept. We know absolute value as the distance a number is from zero We have yet to use the arithmetic involved when solving for an interior variable Today we’re going to talk about this concept on our path to further discussion of inequalities.

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9.4 – Solving Absolute Value Equations and Inequalities

9.4 – Solving Absolute Value Equations and Inequalities. Absolute Value Equations. 1. 2. 3. 4. Absolute Value Inequalities. Absolute value inequalities are solved in the same way linear inequalities are solved. Change the inequality to an equality and solve.

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Absolute-Value Equations and Inequalities

Absolute-Value Equations and Inequalities. Mental Math Solving. Think  What values could x be that would make the equation true? HINT: There are two! ANSWER: 5 or -5. Mental Math Solving (More Example).  x = 7 or -7  x = 9 or -9  x = 18 or -18. Solving an Absolute-Value Equation.

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Solving Absolute Value Equations and Inequalities 1.7

Solving Absolute Value Equations and Inequalities 1.7. The absolute value car ride. What is absolute value? What symbol is used to show absolute value? How do you transform an absolute value inequality and know you have the signs going in the right direction?.

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Solving Absolute Value Equations and Inequalities

Solving Absolute Value Equations and Inequalities. By Ellie Silverman. Solving Absolute Value Equations. 2 x + 3 = 7. 2 x + 3 = 7. These are absolute value signs. This equation means the absolute value of 2x+3 is 7.

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Solving Absolute Value Equations & Inequalities

Solving Absolute Value Equations & Inequalities. Absolute Value (of x ). Symbol Represents the distance x is from zero on the number line. Always positive Ex:. -4 -3 -2 -1 0 1 2. Ex:. What are the possible values of x?

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5.6 Solve Absolute Value Inequalities

5.6 Solve Absolute Value Inequalities. You will solve absolute value inequalities. Essential question: How do you solve absolute value inequalities?. You will learn how to answer this question by rewriting absolute value inequalities as compound inequalities and solving them. a.

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3.7 Absolute Value Equations and Inequalities

3.7 Absolute Value Equations and Inequalities. I can solve equations and inequalities involving absolute value. What are the solutions of |x| + 2 = 9 Solve using inverse operations |x| = 7 so… what is x? x = 7 or x = -7 Why?. Solving an Absolute Value Equation. What about |2x – 5| = 13?

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Absolute-Value Equations and Inequalities

Absolute-Value Equations and Inequalities. 9.3. Equations with Absolute Value Inequalities with Absolute Value. Warm Up. Solve and graph each compound inequality. 1. -3x – 4 < -16 and 2x - 5 < 15 2. 4x + 2 > 10 or -2x + 6 > 16 3. 5 < -3x+2 < 8 4. 2x < -2 and x + 3 > 6

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Solving Absolute Value Equations & Inequalities

Solving Absolute Value Equations & Inequalities. Absolute Value (of x). Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l=3. -4 -3 -2 -1 0 1 2. Ex: x = 5. What are the possible values of x?

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Solving Absolute Value Equations Solving Compound/Absolute Value Inequalities

Solving Absolute Value Equations Solving Compound/Absolute Value Inequalities. Lessons 1-4 and 1-6. Content Objectives. Solve Absolute Value Equations Apply definition to solve, including ‘2’ possible equations Recognize when there is no solution Solve Compound Inequalities

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3-7 Absolute Value Equations AND Inequalities

3-7 Absolute Value Equations AND Inequalities. Objective: To solve equations and inequalities involving absolute value. 3-7 Absolute Value Equations AND Inequalities. Solve equations and inequalities that contain absolute value by:

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1.6 – Absolute Value Equations and Inequalities

1.6 – Absolute Value Equations and Inequalities. Students will be able to: Write and solve equations and inequalities involving absolute value. Lesson Vocabulary Absolute value Extraneous solution. 1.6 – Absolute Value Equations and Inequalities.

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Absolute Value Equations and Inequalities

Check: | a | – 3 = 5 | 8 | – 3 5 Substitute 8 and –8 for a . |–8| – 3 5 8 – 3 = 5 8 – 3 = 5. Absolute Value Equations and Inequalities. Lesson 4-6. Additional Examples. Solve and check | a | – 3 = 5. | a | – 3 + 3 = 5 + 3 Add 3 to each side.

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1-5 Absolute Value Equations and Inequalities

1-5 Absolute Value Equations and Inequalities. Algebraic Definition of Absolute Value - If x > 0, then | x | = x - If x < 0. then | x | = -x. –3 x = –9 –3 x = –21 Subtract 15 from each side of both equations. Check: |15 – 3 x | = 6 |15 – 3 x | = 6

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Chapter 2: Equations and Inequalities 2.5A: Absolute-Value Inequalities

Chapter 2: Equations and Inequalities 2.5A: Absolute-Value Inequalities. Essential Question: What is the procedure used to solve an absolute value equation of inequality?. 2.5A: Absolute-Value Inequalities.

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Absolute Value Equations and Inequalities

Absolute Value Equations and Inequalities. ALGEBRA 1 LESSON 10-5. (For help, go to Lessons 1-3 and 1-4.). Simplify. 1. |15| 2. |–3| 3. |18 – 12| 4. –|–7| 5. |12 – (–12)| 6. |–10 + 8| Complete each statement with <, =, or >. 7. |3 – 7| 4 8. |–5| + 2 6

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More Related

Mastering Absolute Value Equations and Inequalities: A Comprehensive Guide

Mastering Absolute Value Equations and Inequalities: A Comprehensive Guide

Presentation Transcript

1.6 Absolute-Value Equations &amp; Inequalities

2.2 Solve Absolute Value Equations and Inequalities

9.2 Absolute Value Equations and Inequalities

Solve absolute Value Inequalities

Absolute Value Equations and Inequalities

Solve absolute value equations

9.4 – Solving Absolute Value Equations and Inequalities

Absolute-Value Equations and Inequalities

Solving Absolute Value Equations and Inequalities 1.7

Solving Absolute Value Equations and Inequalities

Solving Absolute Value Equations &amp; Inequalities

5.6 Solve Absolute Value Inequalities

3.7 Absolute Value Equations and Inequalities

Absolute-Value Equations and Inequalities

Solving Absolute Value Equations &amp; Inequalities

Solving Absolute Value Equations Solving Compound/Absolute Value Inequalities

3-7 Absolute Value Equations AND Inequalities

1.6 – Absolute Value Equations and Inequalities

Absolute Value Equations and Inequalities

1-5 Absolute Value Equations and Inequalities

Chapter 2: Equations and Inequalities 2.5A: Absolute-Value Inequalities

Absolute Value Equations and Inequalities

1.6 Absolute-Value Equations & Inequalities

Solving Absolute Value Equations & Inequalities

Solving Absolute Value Equations & Inequalities