Absolute Value Inequalities Algebra Solving an AbsoluteValue Inequalities

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Absolute Value Inequalities Algebra

Absolute Value Inequalities Algebra

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

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

Graphing Absolute Value • When an absolute value is greater than the variable you

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.

Solving an Absolute-Value Inequality Solve |x 4|<3 x 4 IS POSITIVE |x 4| 3

Solving an Absolute-Value Inequality Solve |x 4|<3 x 4 IS POSITIVE |x 4| 3 x 4 3 x 7 x 4 IS NEGATIVE |x 4| 3 x 4 3 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.

Solving an Absolute-Value Inequality 1 POSITIVE | 3 6 and graph 2 x +

Solving an Absolute-Value Inequality 1 POSITIVE | 3 6 and graph 2 x + 2 x 1 IS 2 x +the 1 solution. IS NEGATIVE | 2 x 1 | 3 6 | 2 x 1 | 3 6 2 x + 1 IS POSITIVE 2 x + 1 IS NEGATIVE | 2 x 1| 31 |6 9 | 2 x 1| 31 |6 9 2 x 1 |1 | 2 x 9 +9 | 2 x 1 | 9 2 x 10 2 x 8 2 x 1 9 2 x 1 +9 x 4 x 5 Solve | 2 x 10 2 x 8 The solution is all real numbers greater than or equal x 4 x 5 Reverse to 4 or less than or equal to 5. This can be written as inequality the compound inequality x 5 or x 4. symbol. 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

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

Absolute Value Inequalities Algebra