WARM UP MULTIPLE CHOICE Which inequality is true? a)-9 > -5 b)9 < 5 c)9 < -5 d)-9 < 5 Which number is less than –0.1? a)-10 b)0 c)0.001 d)10 3

WARM UP MULTIPLE CHOICE Which inequality is true? a)-9 > -5 b)9 < 5 c)9 < -5 d)-9 < 5 Which number is less than –0.1? a)-10 b)0 c)0.001 d)10 2

WARM UP MULTIPLE CHOICE Which inequality is true? a)-9 > -5 b)9 < 5 c)9 < -5 d)-9 < 5 Which number is less than –0.1? a)-10 b)0 c)0.001 d)10 1

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

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

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. 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 Absolute Value

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 Value Evaluate the expression a. a. І5І b. І-2.3І c. –І1/2І d. -І-8ІSolution a)І5І b)І-2.3І c)–І1/2І d)-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)І0І c)І3/2І d)-І1.7І

EXAMPLE 3: Solve an Absolute Value Equation Use mental math to solve the equation. a. a. ІxІ = 7 b. ІxІ = 5.1c. ІxІ = -2/9Solution a)ІxІ = 7 b)ІxІ = 5.1 c)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 = -4 b)ІxІ = 1.5 c)ІxІ = 1/6