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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 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

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 2.2 Absolute Value • GOAL: Find the opposite and the absolute value of a number. • KEY WORDS: • Opposite • Absolute Value • Counterexample

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. 2.2 Absolute Value CHECKPOINT Evaluate the expression. І-4І І0І І3/2І -І1.7І

  11. 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.

  12. 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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