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

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.

Solve for x
l 5x l = 40

• x = 8

  x =-8

• x = 35

  x = -35

• x = 8

• No Solution

Solve for x
l 2x−1 l = 9

• x = 5

  x =-4

• x = 5

  x = -5

• Only x = 5
• No Solution

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

• x = -14

• x = -4

• x = -14

  x = -4

• No Solution

| x – 3 |= 0

• x = 3

• x = -3

• x = -3

  x = 3

• No Solution

∣ 2x + 9 ∣ = 15

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

Solve:

• x = 24

• x = -6

  x = -8

• x = 16

  x = 4

• x = 24

  x = -24

• x = 4

  x = -4

• x = 9

  x = -9

• x = 5

  x = -9

• x = 13

  x = -1

Solve for x
l 2x−1 l = 9

• x = 5

  x =-4

• x = 5

  x = -5

• Only x = 5
• No Solution