Absolute Value Equations and Inequalities OBJECTIVE: TSWBAT write and solve an absolute value inequality

Key Concept The absolute value of a real number x, written |x|, is the distance from zero on the number line. |4| = 4 |-4| = 4

So If we have |x| = 5 then what can x be? X can equal 5 X can also be -5 Because |5| = 5 and |-5| = 5

A Little More |x| = 8 x = 8 or x = -8 Tru dat? What if we replaced x with x-2 then |x – 2| = 8 So x – 2 = 8 or x – 2 = -8 x = 10 or x = -6

a.Start with |m| = 5 replace m with m-3 |m-3| = 5 m-3 = 5 or m – 3 = -5 And m = 8 or m = -2 How about |z + 4| = 12

What is the solution of |2x – 1| = 5? So we have 2 possibilities for |2x – 1| = 5 possibility #12x – 1 = 5 2x = 6 x = 3 or possibility #2 2x – 1 = -5 2x = -4 x = -2 So x = 3 or x = -2

Try this

Classwork/Homework 1-6A 1.|x – 4| = 12.|2x + 3| = 5 3. |2x + 7| = 234.|3x + 2| = 4 5. |3x + 2| = -66.|5x – 1| = 9 7. |3x – 5| = -88.|x – 3| = 11 9.|6x – 2| = 1010.|7x – 10| = 11

Solving multi-Step Absolute Value Equations What is the solution of 3|x + 2| - 1 = 8? Notice before the absolute value expression was alone. In this problem it is not. Our first job is to get the absolute value expression alone. So we will add 1 then divide by 3 3|x + 2| - 1 = |x + 2| = 9 |x+2| = 3 Now we have 2 possibilities #1x + 2 = 3 and #2x + 2 = -3 And x = 1 or x = -5

Your turn use the markers and your desk top What is the solution of 2|x + 9| + 3 = 7 ? Subtracting 3 and dividing by 2 2|x + 9| = 4 |x + 9| = 2 Now the 2 possililities x + 9 = 2 or x + 9 = -2 and x = -7 or x = -11

Assignment 1.6 Absolute Value Equations 1. |-6x| = 242.|2x + 8| - 4 = 12 3.|x-2| = 4x + 84.|x – 3| = 9 5.|3x| = 186.2|3x – 2|= 14 7.|2x – 3| = -18.|y - 5| - 2 = 10 9.|2z – 3| = 4z – 110.|2y – 4| = |2x + 5| = 3x |4 – 8b| = |3x – 1| + 10 = |6 – 5x|= 15x – |3x – 7|= 10x - 8