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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

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 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

- GOAL: Find the opposite and the absolute value of a number.
- KEY WORDS:
- Opposite
- Absolute Value
- Counterexample

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

- 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

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.

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.

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.

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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