Absolute Value Equations

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

|8 - 4x| = 16

• x = -2, x = -6
• x = 2 , x = 24
• x = -2, x = 6
• No Solution

Solve |x – 12| - 3 = 11.

• -2, -26
• -2, 26
• 3, 25
• 4, -7

Solve for x
2 lx−4l+8=18

• x = 9 and x =-1
• x = 1 and x = -9
• x= 4 and x = -2
• No Solution

| 3x - 6 | - 9 = -3

• No Solution
• x = 0 and x = 4
• x = 2 and x = -2
• x = -4 and x = 4

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4
• x = 5 and x = -5
• Only x = 5
• No Solution

Solve the following equation:

|2x – 3| + 5 = 10.

• {−1, 1}

• {−1, 4}

• {−1, −4}

• {1, 4}

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