Absolute Value Equations

Solve for x
l 5x l = 40

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

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

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

-|−2r − 1| = 11

• {-6,5}
• {5,-6}
• -6
• No Solution

|v + 8| − 5 = 2 

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

−2|−2r − 4| = -12

• {3,1}
• {-3,-1}
• {-3}
• No Solution

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• 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.