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MULTIPLE CHOICE Which inequality is true?a) -9 > -5b) 9 < 5c) 9 < -5d) -9 < 5Which number is less than –0.1?e) -10f) 0g) 0.001h) 10

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WARM UP

MULTIPLE CHOICE Which inequality is true?a) -9 > -5b) 9 < 5c) 9 < -5d) -9 < 5Which number is less than –0.1?e) -10f) 0g) 0.001h) 10

2

WARM UP

MULTIPLE CHOICE Which inequality is true?a) -9 > -5b) 9 < 5c) 9 < -5d) -9 < 5Which number is less than –0.1?e) -10f) 0g) 0.001h) 10

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MULTIPLE CHOICE Which inequality is true?a) -9 > -5b) 9 < 5c) 9 < -5d) -9 < 5Which number is less than –0.1?e) -10f) 0g) 0.001h) 10

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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.

0

-3 3

EXAMPLE 1: Find the Opposite of a NumberUse 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.

2.2 Absolute Value

0-4 4

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.

EXAMPLE 2: Absolute ValueEvaluate the expression

a. І5І b. І-2.3І c. –І1/2І d. -І-8І Solutiona) І5І b) І-2.3Іc) –І1/2Іd) -І-8І

2.2 Absolute Value

*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.

a) І-4І b) І0Іc) І3/2Іd)-І1.7І

EXAMPLE 3: Solve an Absolute Value EquationUse mental math to solve the equation.

a. ІxІ = 7 b. ІxІ = 5.1 c. ІxІ = -2/9Solutiona) ІxІ = 7 b) ІxІ = 5.1c) ІxІ = -2/9

2.2 Absolute Value

*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.

a) ІxІ = -4b)ІxІ = 1.5c) ІxІ = 1/6