Absolute Value Equations

−2|−2r − 4| = -12

• {3,1}
• {-5,1}

• {-3}
• No Solution

|2a - 10| = 6

• a = 8, a = 5
• a = 2
• a = 8
• a = 8, a = 2

| x – 3 |= 0

• 3
• -3
• {-3, 3}
• no solution

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.

3| −8x| + 8 = 80

• {-7/3, 7/3}
• {-3,3}
• {11/3,-11/3}
• No Solution

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0
• x = 3 and x = -3
• x = -12 and x = 0
• No Solution

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

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• 
• 

• Cancel the 7 by subtracting 7 on both sides of the equation.

• Cancel the -5 by adding 5 on both sides of the equation.

• Cancel the 47 by subtracting 47 on both sides of the equation.

• Cancel the -5 by dividing by -5 on both sides of the equation.