Compound Absolute Value Inequalities and Equations

How many solution(s) an absolute value equation has if it is equal to zero?

• 1

• 2

• No Solution

How many solution(s) an absolute value equation has if it is equal to a positive number?

• 1

• 2

• No Solution

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

• -14

• -4

• {-14, -4}

• no solution

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? 

• Drop the absolute value bars by splitting into two inequalities 

• Drop the absolute value bars and subtract 7 from both sides

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

• x + 7 > 1 AND

  
  

  x + 7 > -1

• x + 7 > 1

• x + 7 > 1 OR

  X + 7 < -1

-2 < x - 9 < 3

• x < 12

• 7 < x

• 7 < x < 12

Solve:  -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3

• -1 < x < 3

• 1 < x < 3

• 1 ≤ x ≤ 3

3x-4< -13 or 7x+1> 22

• All Real numbers

•   x>3   and x>-9

• The answer is not listed

• x<-3   or x>3

Write an inequality for Graph 4.

• -2 < x < 5

• x < -2 or x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x ≤ 5