Solving Absolute Value Equation Notes by majenkins2012


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									Algebra II Notes
Solving Absolute Value Equations (Day 1)

The absolute value of a number x, written |x|, is the          x, if x is positive
distance of a number from zero on a number line. The     |x| = 0, if x=0
formal definitions of absolute value is shown in the box
                                                               -x, if x is negative
to the right.
Solve a simple absolute value equation and interpret the meaning:

Ex 1   (a) |x| = 3

            There are two numbers that have a distance of 3 from zero.
                       3        3

           -3    -2 -1     0   1 2 3

            So the solutions to the equation |x| = 3 are                    and

       (b) |x-5| = 7

           This equation wants you to find the numbers that have a distance of 7 units from 5.
           The value of 7 is referred to as the “tolerance” value. Draw a number line to find the

           Solving an absolute value equation algebraically requi
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