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Solving Linear and Absolute Value Inequalities: Techniques and Insights

This guide covers the essentials of solving linear inequalities and absolute value inequalities, including definitions and examples. Learn about the rules for adding, subtracting, multiplying, and dividing inequalities, and how these differ when involving negative numbers. Discover graphing techniques and interval notation for expressing solutions neatly. Explore compound inequalities (both conjunction and disjunction) and understand the implications of absolute value in inequalities. Get insights on finding solutions and the conditions under which no solutions occur.

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Solving Linear and Absolute Value Inequalities: Techniques and Insights

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    1. Section 2.6 Solving Linear Inequalities and Absolute Value Inequalities

    2. Inequality Inequality- a statement that two quantities are not equal. Uses the signs: < , >, , , Linear Inequality ex. 3x + 10 15

    3. Solution to Inequality Equation Finite number of solutions Inequality Infinite Solutions

    4. Adding and Subtracting Inequalities Rules are the same as when solving equations: What you add/subtract to one side of the inequality you must do to the other side to make an equivalent inequality.

    5. Multiplying and Dividing Inequalities Rules are the same as when solving equation EXCEPT when negative numbers are involved. Rule: When solving inequalities, multiplying and/ or dividing by the same negative number reverses (flips) the direction of the inequality the sign.

    6. Graphing Inequalities

    7. Interval Notation [ , ] number is included ( , ) number is not included ( , ) always used with ,

    10. Compound Inequalities Conjunction (Intersection) And -3 < 2x + 5 and 2x + 5 < 7 can also be written -3 < 2x + 5 < 7 Solution: Values they share Disjunction (Union) Or 2x < 8 or 2x + 4 > 3

    13. Absolute Value Equations Absolute Value Equations ex.

    14. Meaning of Absolute Value Equation What does it mean? or

    15. Absolute Value Inequalities Absolute Value Inequalities

    16. Meaning of Absolute Value Inequalities What do they mean?

    19. Absolute Value Answer is always positive Therefore the following example cannot happen. . . Solutions: No solution

    20. Absolute Value Answer is always positive Therefore the following example can happen. . . Solution:

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