Absolute Value. That was easy

Transcription

1 Absolute Value The absolute value of a number is its distance from 0 on a number line. Absolute value is always nonnegative since distance is always nonnegative. Let s write an example using mathematical symbols. 4 4 or 4 4 Now let s see what that looks like on a number line. 4 units 4 units That was easy

2 Solving Absolute Value Equations x x x 3 3or x 3 7 x x 2 2or x 2 x x x 6 6or x 6 2x 5 11 That was easy 2x 5 11 or 2x x 16 2x x 8 or x 3

3 More Absolute Value Equations x 2 x x x 3 3or x 3 7 x x 3 no solution x 5 x x 4 4or x 4 6 x x 4 no solution Asi de Facil

4 Practice Problems x x 3 7 3x 9 x 8 5 x 4 x 3 x 8 5or x or x 4 x 3or x 3 x 3 or x 13 4x x 1 7 4x 1 7 or 4x 1 7 4x 8or 4x 6 x 2or x x 12 x 3 no solution That was easy

5 Homework Page 211: Even Numbers

6 Absolute Value Inequalities x 2 That means the distance from zero is less than 2 units. x 2 That means the distance from zero is more than 2 units x is between the points. x is split on either side of the points. If ax b d then d ax b d Between If ax b d then ax b d or ax b d Split

7 Absolute Value Inequalities with Less Than 2x 1 7 Less than means between Remove the absolute value symbol and write the equation according to the rules. Solve both sides of the inequality at the same time. Graph your solution on a number line. 7 2x x x That was easy

8 Absolute Value Inequalities with Greater Than 4x 2 10 Greater than means split Remove the absolute value symbol and write the equation according to the rules. Solve both inequalities. Graph your solution on a number line That was easy 4x 2 10 or 4x x x 2 or 4x x 3

9 More Absolute Value Inequalities 3x x x x x 5 3 2x 5 3 or 2x x 8 2x x 4 or x That was easy Asi de facil

10 Homework Page 211: Even Numbers

11 Absolute Value Equation Word Problem Gertrude is sitting on a bench. From 100 feet away, Betty rides her bike toward her and then passes her. Betty rides at a constant speed of 20 feet per second. Her distance d from Gertrude in feet after t seconds is given by the following equation. d t At what times is Betty 40 feet from Gertrude? t t 40 or t 40 20t 60 t 3 40 feet 40 feet 20t 140 t 7 Betty is 40 feet from Gertrude at 3 seconds and at 7 seconds. I knew this was coming. Asi de Facil

12 Absolute Value Inequality Word Problem The ideal weight of a bag of chips is 8.75 ounces. The actual weight may vary from the ideal weight by at most 0.05 ounces. Find the range of acceptable weights for a bag of chips. Let x = actual weight Don t do that. Let me show you how easy it is. x x x I d rather stick a pencil in my eye than try to solve this equation. That was easy The chips can weigh between 8.7 ounces and 8.8 ounces.

13 Another Absolute Value Inequality Word Problem In a poll for an upcoming mayoral election, 38% of voters say they would vote for Stella Studebaker. The poll has a margin of error of plus or minus 2 percentage points. Use the following inequality to find the least and greatest percent of voters, v, that will vote for Stella. v 38 2 Don t do that. Let me show you how easy it is. Let me get my pencil ready. v v v v Asi de facil At least 36%, but not more than 40% will vote for Stella.

14 Yet Another Absolute Value Inequality Word Problem A car manufacturer aims to manufacture 135 cars a day. The ideal number of cars manufactured can vary by up to 26 cars a day. What are the minimum and maximum number of cars that can be manufactured in a day? Let x = ideal number of cars Don t do that. Let me show you how easy it is. x x x I might be sticking my pencil in my eye after all. That was easy They manufacture between 109 and 161 cars a day.

15 Homework Page 212: 63, 68, 70, 75, 76