Absolute Value Equations and Inequalities

|v + 8| − 5 = 2 

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

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

• -14
• -4
• {-14, -4}
• no solution

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve |x – 12| - 3 = 11.

• -2, -26
• -2, 26
• 3, 25
• 4, -7

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

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

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 the absolute value alone by dividing both sides by 5
• Drop the absolute value bars and add 7 and 5 together
• Get the absolute value alone by subtracting 5 from both sides

After you split into two inequalities, what would they look like? 

• x + 7 > 1        
     
  x + 7 > -1
• x + 7 > 1
• x + 7 > 1
  X + 7 < -1

|v + 8| − 5 = 2 

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