Solving Equations Involving Absolute Values

∣ 2x + 9 ∣ = 15

• x = 3 
• x = 3
  x = -6
• x = 3
  x = -12
• x = 6
  x = -12

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• 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

Solve |2x –3| + 5 =10.

• -1, 1
• -1, 4
• -1, -4
• 1, 4

Solve |2x –3| + 5 =10.

• -1, 1
• -1, 4
• -1, -4
• 1, 4

|x+19|=25

• -6, 44
• 6, -44
• 6
• No Solution

5∣ x ∣ - 8 = 2

• x = 5
  x = 2
• x = 2
  x = 6/5
• x = -5
  x = 10
• x = 18
  x =  -18

Sam's house is 14 blocks from the school. Emily lives 6 blocks from Sam. Which equation represents the location of Emily's house in relation to the school?

• |x + 6| = 10
• |x – 6| = 14
• |x – 14| = 6
• |x + 14| = 6

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.