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Absolute Value Inequalities

Absolute Value Inequalities. Algebra. Solving an Absolute-Value Inequalities.  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8.

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Absolute Value Inequalities

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  1. Absolute Value Inequalities Algebra

  2. Solving an Absolute-Value Inequalities  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8

  3. Graphing Absolute Value • When an absolute value is greater than the variable you have a disjunction to graph. • When an absolute value is less than the variable you have a conjunction to graph.

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

  5. Solving an Absolute-Value Inequality 2x + 1 IS POSITIVE 2x + 1 IS NEGATIVE | 2x  1 | 3  6 | 2x  1 | 3  6 | 2x  1 |  9 | 2x  1 |  9  2x  1  9 2x  1  +9 2x 10 2x  8 x  4 x 5  6  5  4  3  2  1 0 1 2 3 4 5 6 Solve | 2x  1| 3  6 and graph the solution. 2x + 1 IS POSITIVE 2x + 1 IS NEGATIVE | 2x  1 | 3  6 | 2x  1 | 3  6 | 2x  1 |  9 | 2x  1 |  9 2x  1  9 2x  1  +9 2x 10 2x  8 The solution is all real numbers greater than or equal to 4orless than or equal to 5. This can be written as the compound inequality x  5orx 4. x  4 x 5 Reverse inequality symbol. 4. 5

  6. Strange Results True for All Real Numbers, since absolute value is always positive, and therefore greater than any negative. No Solution Ø. Positive numbers are never less than negative numbers.

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