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WARM UP. 3. MULTIPLE CHOICE Which inequality is true? -9 > -5 9 < 5 9 < -5 -9 < 5 Which number is less than –0.1? -10 0 0.001 10. WARM UP. 2. MULTIPLE CHOICE Which inequality is true? -9 > -5 9 < 5 9 < -5 -9 < 5 Which number is less than –0.1? -10 0 0.001 10. WARM UP.

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Warm up
WARM UP

3

MULTIPLE CHOICE

Which inequality is true?

-9 > -5

9 < 5

9 < -5

-9 < 5

Which number is less than –0.1?

-10

0

0.001

10


Warm up1
WARM UP

2

MULTIPLE CHOICE

Which inequality is true?

-9 > -5

9 < 5

9 < -5

-9 < 5

Which number is less than –0.1?

-10

0

0.001

10


Warm up2
WARM UP

1

MULTIPLE CHOICE

Which inequality is true?

-9 > -5

9 < 5

9 < -5

-9 < 5

Which number is less than –0.1?

-10

0

0.001

10


Warm up3
WARM UP

0

MULTIPLE CHOICE

Which inequality is true?

-9 > -5

9 < 5

9 < -5

-9 < 5

Which number is less than –0.1?

-10

0

0.001

10


2.2 Absolute Value

  • GOAL: Find the opposite and the absolute value of a number.

  • KEY WORDS:

  • Opposite

  • Absolute Value

  • Counterexample


2.2 Absolute Value

Two numbers that are the same distance from 0 on a number line but on opposite sides of 0 are opposites.

The numbers -3 and 3 are opposites because each is 3 units from 0.

-3

3

0


2.2 Absolute Value

  • EXAMPLE 1: Find the Opposite of a Number

  • Use a number line to find the opposite of -4.

  • Solution

  • You can see that -4 is 4 units to the left of 0. The opposite of -4 is 4 unites to the right of 0. So the opposite of -4 is 4.

-4

4

0


2.2 Absolute Value

ABSOLUTE VALUE The absolute value of a number is its distance from zero on a number line. The symbol ІaІ represents the absolute value of a.


2.2 Absolute Value

EXAMPLE 2: Absolute Value

Evaluate the expression

a. І5Іb. І-2.3Іc. –І1/2Іd. -І-8І

Solution

І5І

І-2.3І

–І1/2І

-І-8І

*If a is positive, then ІaІ= a

*If a is negative, then ІaІ= -a. Use the definition or opposites.

*The absolute value of ½ is ½. Use the definition of opposites.

*The absolute value of -8 is 8. Use the definition of opposites.


2.2 Absolute Value

CHECKPOINT

Evaluate the expression.

І-4І

І0І

І3/2І

-І1.7І


2.2 Absolute Value

EXAMPLE 3: Solve an Absolute Value Equation

Use mental math to solve the equation.

a. ІxІ = 7 b. ІxІ = 5.1 c. ІxІ = -2/9

Solution

ІxІ = 7

ІxІ = 5.1

ІxІ = -2/9

*Ask, “What numbers are 7 units from 0?” Both 7 and -7 are 7 units from 0, so there are two solutions: 7 and -7.

*Ask, “What numbers are 5.1 units from 0?” Both 5.1 and -5.1 are 5.1 units from 0, so there are two solutions: 5.1 and -5.1

*The absolute value of a number is never negative, so there is no solution.


2.2 Absolute Value

CHECKPOINT

Use mental math to solve the equation. If there is no solution, write no solution.

ІxІ = -4

ІxІ = 1.5

ІxІ= 1/6


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