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# Absolute Value

### Absolute Value Equations & Inequalities

TRUE OR FALSE: An absolute value equation can equal 0. FALSE
|x| = A is equivalent to: X = A OR X = -A
|x| < A is equivalent to: -A < X < A
|x| > A is equivalent to: X < -A OR X > A
SOLVE: |x + 4| = -8 NO SOLUTION Absolute value's are always positive, and can not equal anything negative.
SOLVE: |x + 8| < -4 NO SOLUTION Absolute value's are always positive, and can never be less than a negative number.
SOLVE: |x| > -6 (-infinity,infinity) No matter what x's value is, it will always be positive, which is greater than a negative.
SOLVE: |x| > 4 (-infinity,-4)U(4,infinity) Any number (negative or positive) greater than 4 is a solution. Parenthesis are used to denote the solution is NOT EQUAL TO.
SOLVE: |x| < 5 -5 < x < 5
SOLVE: |x + 2| > 6 x + 2 > 6 OR x + 2 < -6 x > 4 OR x < -8 (-infinity,-8)U(4,infinity)
Created by: along500