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Understanding Absolute Value Equations: A Comprehensive Review

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In this unit on absolute value equations, we explore the concept of absolute value, defined as the distance of a number from zero on a number line. With practical examples, we learn how to solve absolute value equations by isolating the absolute value expression and splitting the problem into two cases. Through step-by-step guidance, we cover various equations and emphasize that not all absolute value equations have solutions, particularly those resulting in negative values. Homework exercises are included for practice.

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Understanding Absolute Value Equations: A Comprehensive Review

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  1. Absolute Value Equations Unit 3, Day 5

  2. Review of Absolute Value http://www.brainpop.com/math/numbersandoperations/absolutevalue/preview.weml

  3. 5units The absolute-value of a number is that numbers distance from zero on a number line. For example, |–5| = 5. 1 6 4 3 0 1 2 3 4 5 5 2 6 Both 5 and –5 are a distance of 5 units from 0, so both 5 and –5 have an absolute value of 5.

  4. How to Solve Absolute Value Equations: Isolate the absolute-value expression Split the problem into two cases.

  5. Solve the equation. |x| –3 = 4 + 3 +3 |x| = 7 x = 7 –x = 7 –1(–x) = –1(7) x = –7

  6. Solve and check |a| – 3 = 5 |a| – 3 + 3 = 5 + 3Add 3 to each side. |a| = 8 Simplify. a = 8 or a = –8

  7. +2 +2 Solve the equation. |x 2| = 8 x 2= 8 x 2= 8 +2 +2 x = 10 x = 6

  8. Solve |3c – 6| = 9 3c – 6 = 9 3c – 6 = –9

  9. |x + 7| = 8 x + 7 = –8 x + 7 = 8 – 7 –7 – 7 –7 x = –15 x = 1

  10. CAREFUL! Not all absolute-value equations have solutions. If an equation states that an absolute-value is negative, there are no solutions.

  11. Solve the equation. 2  |2x 5| = 7 2 2  |2x 5| = 5 1 1 |2x  5| = 5 Absolute values cannot be negative. This equation has no solution.

  12. Homework p.237, #1-21

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