1.6 ABSOLUTE VALUEEQUATIONS ANDINEQUALITIESPart 1: Absolute Value Equations
ABSOLUTE VALUE The absolute value of a real number x, written |x|, is its distance from zero on the number line Example:|5| =5 |-5| = 5
ABSOLUTE VALUES EQUATION An absolute value equation is an equation that has a variable inside the absolute value sign Absolute value equations can have two answers because opposites have the same absolute value.
SOLVING ABSOLUTE VALUEEQUATIONS To solve an absolute value equation: 1. Isolate the absolute value 2. Remove the absolute value signs and set up as shown: x =k x = − k or x = k 3. Check your answers!
SOLVE EACH EQUATION.GRAPH THE SOLUTION.2x −1 = 5
SOLVE EACH EQUATION.GRAPH THE SOLUTION.3x + 2 = 4
SOLVE EACH EQUATION.GRAPH THE SOLUTION.3 x + 2 −1 = 8
SOLVE EACH EQUATION.GRAPH THE SOLUTION. 2 x+9 +3= 7
SOLVE EACH EQUATION.GRAPH THE SOLUTION.
EXTRANEOUS SOLUTIONS An extraneous solution is a solution derived from an original equation that is not a solution of the original equation. Remember that the absolute value measures the distance from zero on a number line. Distance can never be negative. Therefore, we must check our answers when working with absolute values.
SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS. x + 2 = 8x
SOLVE AND CHECK FOREXTRANEOUS SOLUTIONS.3x + 2 = 4 x + 5