L ESSON 1-6 A BSOLUTE V ALUE E QUATIONS AND I NEQUALITIES The absolute value of a real number x, written |x|, is it distance from 0 on the number line. |4|= 4|− 4|= 4 An absolute value equation has a variable within the absolute value sign. For example, |x|= 5. In this case the value of x can be 5 or − 5 since |5|and |− 5|both equal 5. Since the opposites have the same absolute value, an absolute value equation can have two solutions

S OLVING AN A BSOLUTE V ALUE E QUATION, P AGE 42, E XAMPLE 1 |3x + 2 |= 4 3x + 2 = 43x + 2 = − 4 x = 2/3 x = − 2

S OLVING A MULTISTEP A BSOLUTE V ALUE E QUATION, P AGE 42 2 |x + 9 |+ 3 = 7 2 |x + 9 | = 4 |x + 9 | = 2 x + 9 = 2x + 9 = − 2 x = − 7x = −11

A BSOLUTE V ALUE E QUATIONS |x|= −5 has no solution. Distance on a number line cannot be negative. Distance cannot be negative. An extraneous solution is a solution derived from an original equation that is not a solution of the original equation. Plug all solutions found back into the original equation to check to see solutions are relevant. |x|= −5 has no solution. Distance on a number line cannot be negative. Distance cannot be negative. An extraneous solution is a solution derived from an original equation that is not a solution of the original equation. Plug all solutions found back into the original equation to check to see solutions are relevant.

P ROBLEM 3 PAGE 43, C HECKING FOR E XTRANEOUS S OLUTIONS Demonstrate Got it # 3.

M ORE A BSOLUTE V ALUE I NEQUALITY The solutions of |x| − 5. It means x is the distance of 5 units from “0” from both the positive and negative side of “0”. This is a Compound Inequality. x − 5 Explain “innie” and Line Segment.

A NOTHER E XPLANATION

S OLVING THE A BSOLUTE V ALUE I NEQUALITY |A | < B You can also split the equation in two. |2x − 1|< 5 2x − 1 − 5 x − 2 It’s an “innie” It’s a line segment

S OLVING AN A BSOLUTE V ALUE I NEQUALITY |A|≥ B P AGE 44 If the inequality is ≥, then the graph is an “outie” or 2 opposite rays. What is the difference between ≥ and > with regard to graphing?

P AGE 44 G OT #5

T OLERANCE P AGE 44 Tolerance is a term that is associated with the manufacturing industry. Most manufactured items are created within certain dimensional boundaries or tolerances. Tolerance is ½ the difference of the maximum and minimum acceptable values. Absolute Value equations can be used to describe tolerance.

P AGE 45 E XAMPLE 6 T OLERANCE |h – 52.5| ≤ 0.5

L ESSON C HECK & P ROBLEM S OLVING Lesson Check #1 thru #5 Practice #10, #22, #28, #40, #44 Homework #12 thru #16 Even, #20,#24, #26, #30, #38, #46 thru #56 Even