Absolute-Value Inequalities

Which of the following is the correct graph for the given inequality?

 $\left|3x-2\right|\le5$  

• 
• 
• 
• 

Using the given graph/ inequality, determine the solution.

 $2\left|x-4\right|+3>6$  

•  $x>5.5\ or\ x<2.5$  

•  $x\ge\ 5.5\ or\ x\le2.5$  

•  $2.5<x<5.5$  

•  $2.5\le x\le5.5$  

The answer from #2 was

 $x>5.5\ or\ x<2.5$ . Graph this solution on a number line.

• 
• 
• 
• 

Without graphing, what is the solution to the following inequality?

 $\left|x-3\right|\le-9$  

• All real numbers 

• No solution

•  $x\ge-9$  

•  $x\le-9$  

Without graphing, what is the solution to the following inequality?

 $\left|x-3\right|\ge-9$  

• All real numbers 

• No solution

•  $x\ge-9$  

•  $x\le-9$