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  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8

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.

This can be written as 1  x  7. 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.

Solve | 2x  1 | 3  6 and graph the solution. Solving an Absolute-Value Inequality | 2x  1 |  3  6 | 2x  1 |  9 2x  1  +9 x  4 2x  8 | 2x  1 | 3  6 2x  1  9 2x  10 x  5 2x + 1 IS POSITIVE 2x + 1 IS NEGATIVE 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  8 2x  10 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. x  4 Reverse inequality symbol. x  5  5 4.  6  5  4  3  2  1 0 1 2 3 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.

Absolute Value Inequalities Algebra