M1 2.3: Absolute Value Equations

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

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Defining absolute value

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

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Defining absolute value

• a must be negative

• b must be negative

• c must be negative

• Every absolute value equation will have two solutions

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Defining absolute value

Solve for x
l 5x l = 40

• x = 8 and x =-8
• x = 35 and x = -35
• Only x = 8
• No Solution

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Solving absolute value equations

Solve for x
l 4x−3 l = 17

• x = 5 and x =-3.5
• x = 0 and x = -5
• x = 10 and x = -10
• No Solution

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Solving absolute value equations

|v + 8| − 5 = 2 

• {-1,-15}
• {-1,-5}
• {-15,15}
• No Solution

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Solving absolute value equations

A survey of 500 Asheville residents finds that 62% of respondents are fully vaccinated for COVID-19. If the survey has a margin of error of 3%, which of the following absolute value equations could model the actual amount of fully vaccinated Asheville residents?

• None of these

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Building absolute value equations

It takes approximately 6 minutes for a skydiver to land once they jump from the plane, give or take 30 seconds. What is the range of time, in seconds, that it could take for the skydiver to land? [ _______ , _______ ]

• [-24, 36]

• [330, 390]

• [-670, 1260]

• None of these

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Building absolute value equations

The number line shown below represents the solutions for which absolute value equation?

−2|−2r − 4| = -12

• {5,1}
• {-5, -1}
• {-5, 1}
• No Solution

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Solving absolute value equations