Unit One obj. solve abs.val. Section 1-6 Absolute Value Unit One obj. solve abs.val.

This is asking how far away from 0 is 5 & -5 on the number line In this lesson you will write and solve equations and inequalities involving absolute value. Absolute Value is the distance a number is from zero on a number line. This is asking how far away from 0 is 5 & -5 on the number line 5 4 3 2 1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 Absolute value equation can have two answers, because opposites have the same absolute value.

Solving absolute value The value inside the absolute value can equal 15 or -15 What does x equal??

Solving an Absolute Value Equation Ex) STEPS to solving Abs. Val. Equation Get the absolute value alone Rewrite as two equations Solve check Solving absolute value equation 6:00 video 1 ex) 1 try)

Solving an Absolute Value Equation Check each solution… An extraneous solution is a solution that does not work out when checked in the original problem. Since -3 does not work it is an extraneous solution. The only solution is -1

Practice solving Absolute value equations: Worksheet Practice C – #1,2,5,6 1) 6 & -6 2) 7 & -7 5) 3 & -2 6) 0 & 4 Pg 46 #11-23 odd ANSWERS: ANSWERS: ANSWERS: ANSWERS: Reduce practice problems to allow for enough time

STEPS to solving Abs. Val. inequality Solving an Absolute Value Inequality STEPS to solving Abs. Val. inequality \ Get the absolute value alone Rewrite as two inequalities(flip inequality sign) Solve graph Solving absolute value inequality “OR” 6:30 video 1ex) 1try) AND b/c inequality sign was < -2 3

GreatOR LessthAND Most of the time the original inequality sign will tell you what the graph should look like

Practice Worksheet Practice D- #1,2,5,6 1) y < 0 AND y > -6 2) t ≤ 4 AND t ≥ -1 5) x ≤ ½ and x ≥ -1 6) z > 2 OR z < -2/3 ANSWERS: ANSWERS: ANSWERS: ANSWERS:

Practice Standard Pg. 46 #25-35odd 43-81 Honors Pg. 46 #25-35odd 43-89 Standardized test prep: 90-93 Reduce number of practice problems

LITERAL EQUATIONS Define: literal equation – a literal equation is an equation that uses at least two different variables. Example solve for the indicated variable Circumference of a circle: Perimeter of rectangle: answer answer What is the length of a rectangle with a perimeter of 30ft and the width is 7ft. Distance = rate * time answer If you need to travel 500 miles in 8 hours, what rate should you maintain?

Practice B- #1-4 Answers Answers 1) 2) 3) 4) Answers Answers

Fahrenheit = F and Celsius = C. Example: Fahrenheit = F and Celsius = C. Describe what the formula does. (what’s the input?) Finds Temperature in Celsius given Degrees Fahrenheit. (input is F & output is C) What is F in terms of C? (in other words solve the function for F) What dos this new formula do? (what’s the input?) Answer

Practice F #1-3 1) x=7 2) max: 16.02 3) 513 miles (513.66….) Answers 1) x=7 2) max: 16.02 Min: 15.98 3) 513 miles (513.66….) Answers Answers

Word problems Ex: A 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 “16oz” bottles. What does this mean? If you buy a bottle of 16oz dressing, you might get one that actually has 15.4 to 16.6oz instead.

Ex: A manufacturer has a tolerance of 0 Ex: A manufacturer has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6 lb. Write and solve an absolute value inequality that describes acceptable weights for “9.6 lb” bags. W - 9.6 ≤ 0.36 or w - 9.6 ≥ -0.36 W ≤ 9.96 or w ≥ 9.24 What does this mean?

Practice F #4 & 6 4) 6) Answers Answers