Absolute ValueThe absolute value of a number is its distance from 0 on a number line. Absolute value is always nonnegative since distance is always nonnegative.

44 4 4 or

Let’s write an example using mathematical

symbols. Now let’s see what that looks

like on a number line.

-5 -4 -3 -2 -1 0 1 2 3 4 5

| | |4 units4 units

That was easy

Solving Absolute Value Equations

5 11x 5 5

6x

6 6orx x

2 5 11x

2 5 11x or 2 5 11x 5 5

2 6x 2 2

3x

5 5 2 16x 2 2

8x or

3x

3 3orx x

7 14x 7 7

2x

2 2orx x

That was easy

More Absolute Value Equations

2 5 1x 5 5

2 6x 2 2

3x

3 3orx x

5 20x 5 5

4x

4 4orx x

7 21x 7 7

3x

no solution

6 24x 6 6

4x

no solutionAsi de

Facil

Absolute Value Equation Word Problem

I knew this was coming.

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.100 0d t2

At what times is Betty 40 feet from Gertrude?

10040 20t

100 20 4t 0 or 100 20 0t 4

020t 6

t 3

420t 1 0

t 7Betty is 40 feet from Gertrude

at 3 seconds and at 7 seconds.

Asi de

Facil

| | |40 feet40 feet

Practice Problems3 7 x 3 9 x 8 5 x

4 1 2 5 x4 12 x

4 4

4

o xr

x

x

13

8

3

8 5 5x x

x or x

or3 3

3 o xr

x

x

4 1 7

4 1 7 4 1 7

4 6 4 8

32

2

or

or

or

x

x x

x x

x x

3x

no solution

That was easy

Homework

Page 211: 10 – 30 Even Numbers

Page 212: 63

Absolute Value Inequalities

2x

That means the distance from zero

is less than 2 units.

-2 0 2

2x

That means the distance from zero

is more than 2 units.

x is between the points.

-2 0 2

x is split on either side of the points.

If ax db then

xd da b

Between

If ax db then

ax db or ax db

Split

Absolute Value Inequalities with Less Than

2 1 7x Less than means between

Remove the absolute value symbol and write the equation according to the rules.

2 1x 7 7

Solve both sides of the inequality at the same time.

1 1 1 26 8x

2 2 2

3 4x Graph your solution on a number line.

-3 4

That was easy

Absolute Value Inequalities with Greater Than

4 102x Greater than means split

Remove the absolute value symbol and write the equation according to the rules. 4 02 1x o 4 0r 2 1x

2 2

4 8x 4 4

2x

2 2

4 12x 4 4

3xGraph your solution on a number line.

-2 3

Solve both inequalities.

That was easy

or

More Absolute Value Inequalities

3 14 1x

11 113 4x 4 4 4

15 3 7x 3 3 35 2.33x

2 5 3x or 5 353 2 2x x

5 5 5 5 28 2 2x x

2 2 2 2or4 1x x

-6 0 2 3 6

-8 -4 -1 0 4

That was easy

Asi de facil

Homework

Page 211: 32 – 46 Even Numbers

Solving Absolute Value Inequalities

3.75 1.5x

3.75x 1.5 1.5 3.75 3.75 3.75

2.25 5.25x

7.65 0.25x

7.65x 0.25 0.25 7.65 7.65 7.65

7.4 7.9x

8.625 0.075x

8.625x 0.075 0.075 8.625 8.625 8.625

8.55 8.7x That was

easy

Absolute Value Word ProblemThe 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

I’d rather stick a pencil in my eye than try to solve

this equation.Don’t do that.

Let me show you how easy it is.

8 75 0 05.x .

80 05 0 0575.x. .

8 7 8 8. x .

The chips can weigh between 8.7 ounces and 8.8 ounces.

8.75 8.75 8.75

That was easy

Another Absolute Value 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. 8 23v

Let me get my pencil ready.

Don’t do that. Let me show you

how easy it is.

8 23v

82 3 2v

36 40v

36 40v

At least 36%, but not more than 40% will vote for Stella.

38 38 38 Asi de

facil

Yet Another Absolute Value 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

I might be sticking my pencil

in my eye after all.

Don’t do that. Let me show you

how easy it is.

26135x

1 56 632 2x

109 161x

135 135 135

They manufacture between 109 and 161 cars a day.

That was easy

Homework

Page 212: 68, 69(a only), 70, 75, 76