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 first step?

• Drop the absolute value bars by splitting into two equations
• Add 2 to both sides

What is the first step? 

• Get absolute value alone by subtracting 5 from both sides
• Get absolute value alone by dividing by 5 on both sides
• Split into two equations

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

• -14
• -4
• {-14, -4}
• 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

−2|−2r − 4| = -12

• {3,1}

• {-5,1}

• {-3}

• No Solution

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4
• x = 5 and x = -5
• Only x = 5
• 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