# Absolute Value Equations Objective: Solve equations with an absolute value in them; identify extraneous solutions Essential Question: How do absolute value

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Objective: To solve equations with an absolute value in them by hand & using the calculator Essential Question: How does solving an absolute value equation differ from other equations?

Absolute Value EquationsObjective: Solve equations with an absolute value in them; identify extraneous solutions

Essential Question: How do absolute value bars affect the possible solutions of an equation?

I am 3 miles from my house

|B| = 3B = 3 or B = -3ReviewAbsolute Value: the distance a number is from zero (always positive)

Ex 1) |7| =

Ex 2) |-5| =

Ex 3) 5|2 4| + 2 =Consider the following problem|x + 4| = 7Solving Absolute Value EquationsStep 1: Get bars alone on one side

Step 2: Split up into a positive & negative equation (drop the bars)

Step 3: Solve both equations

Step 4: Check your solution!!! *One of them might be extraneousProblem #13|x + 2| - 7 = 14

3|x + 2| = 21

|x + 2| = 7|x + 2| = 7 x + 2 = 7 x + 2 = -7 x = 5 or x = -9Problem #2|3x + 2| = 4x + 53x + 2 = 4x + 53x + 2 = -4x 5 3x + 2 = 4x + 53x + 2 = -4x 5 Extraneous Solutions solution that you find that is NOT actually a solution

Its a FAKE! |3x + 2| = 4x + 5Problem #3|x 4| + 7 = 2

|x 4| = -5

NO SOLUTION

NO SOLUTIONIf the equivalent value is negative BEFORE YOU DROP THE BARS, there is no solutionProblem #4|x 4| < 10

x 4 < 10x 4 > -10

FLIP SIGNPracticePg.55 #1 11 ODD

Pg.56 #17 23 ODD

You will be turning this inSolving by GraphingStep 1: Enter the left & right side into Y1 & Y2PRESS NUM #1 abs(

Step 2: Find the first intersection

Step 3: Find the second intersection if there is one MATH2nd TRACE#5Problem #13|x + 2| -7 = 14

Problem #2|3x + 2| = 4x + 5

PracticeSolve: |5x| + 10 = 55Solve: |x 3| = 10Solve: 2|y + 6| = 8Solve: |a 5| + 3 = 2 Solve: |4x + 9| = 5x + 18 Tolerance

There are strict height requirements to be a Rockette

You must be between 66 inches 70.5 inchesPerfect AmountLeastAllowedMostAllowedToleranceToleranceProblem #1In a car racing, a car must meet specific dimensions to enter a race. What absolute value inequality describes the heights of the model of race cars with a desirable height of 52 inches, a greatest allowable height of 53 inches, and a least allowable height of 51 inches?Greatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #2A manufacturer has a 0.6 oz tolerance for a bottle of salad dressing advertised as 16oz. Write and solve an absolute value inequality that describes the acceptable volumes for 16 oz.Greatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #3Suppose you used an oven thermometer while baking and discovered that the oven temperature varied between + 5 and -5 degrees from the setting. If your oven is set to 350*, let t be the actual temperature. Write an absolute value inequality to represent the situation. Greatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #4A distributor has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6lb. Write and solve an absolute value inequality that describes acceptable weights for a bag.Greatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #5In a newspaper poll taken before an election, 42% of the people favor the incumbent mayor. The margin of error for the actual percentage p is less than 4%. Find an absolute value inequality that represents this situation.Greatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #6In a wood shop, you have to drill a hole that is two inches deep into a wood panel. The tolerance for drilling a hole is 0.125 inches. What is the shallowest hole allowed?Greatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #7A survey reveals that 78% of people in North Carolina favor a particular law being passed. The margin of error for the actual percentage p is 5%. Write an inequality to model this situationGreatest =Least =Tolerance =Ideal Amount =Actual Amount = Problem #8The normal thickness of a metal structure is 6.5 cm. It expands to 6.54 centimeters when heated and shrinks to 6.46 cm when cooled down. What is the maximum amount in cm that the thickness of the structure can deviate from its normal thickness? Greatest =Least =Tolerance =Ideal Amount =Actual Amount = ##### NOTES: Absolute Value Equations and Inequalities 9/9/2012 آ  NOTES: Absolute Value Equations and Inequalities
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