Solve Absolute Value Inequalities

Solve Absolute Value Inequalities

Essential Question: What are the differences between solving absolute value equations vs. inequalities?

I can solve an absolute value inequality algebraically

Multiple Choice

Which symbol means less than?

• $<$

• $>$

• $\le$

• $\ge$

Multiple Choice

Which symbol means greater than or equal to?

• $<$

• $>$

• $\le$

• $\ge$

Fill in the Blank

Type the correct inequality that would make the statement true.

hint: type in < or >

10 ? 4

Fill in the Blank

Type the correct inequality that would make the statement true.

hint: type in < or >

-7 ? -2

Greater than (>)

Greater than equal to (>)

Remember GREAT "OR"

Less than ( <)

Less than equal to( <)

Remember LESS "AND"

Multiple Choice

Would this absolute value equation be an "AND" or "OR"?
 $\left|x-5\right|\le2$  

• AND

• OR

Multiple Choice

Would this absolute value equation be an "AND" or "OR"?
 $\left|-4x+7\right|\ge3$  

• AND

• OR

Multiple Choice

Would this absolute value equation be an "AND" or "OR"?
 $\left|3x+1\right|<7$  

• AND

• OR

Multiple Select

Which of the following absolute value inequalities would be an "OR"? (CHOOSE ALL THAT APPLY)

•  $\left|4x-1\right|>5$  

•  $\left|-3x+7\right|<11$  

•  $\left|5x+\frac{1}{2}\right|\ge1$  

•  $\left|2x-10\right|\le50$  

•  $\left|7x+5\right|>6$  

Multiple Select

Which of the following absolute value inequalities would be an "AND"? (CHOOSE ALL THAT APPLY)

•  $\left|4x-1\right|>5$  

•  $\left|-3x+7\right|<11$  

•  $\left|5x+\frac{1}{2}\right|\ge1$  

•  $\left|2x-10\right|\le50$  

•  $\left|7x+5\right|>6$  

Multiple Choice

Is this absolute value inequality going to be an "AND" or an "OR"?

 $\left|x+6\right|<2$  

• AND

• OR

Multiple Select

Which two inequalities below would be the next step in solving 

 $\left|x+6\right|<2$  

•  $x+6<-2$  

•  $x+6>-2$  

•  $x+6<2$  

•  $x+6>2$  

•  $x+6=2$  

Multiple Choice

Solve the absolute value inequality.

 $\left|2x-1\right|<3$  

•  $x<-1\ or\ x>2$  

•  $1<x<2$  

•  $-1<x<2$   

•  $-1>x>2$  

Multiple Choice

Is this absolute value inequality going to be an "AND" or an "OR"?

 $9\left|x+4\right|+10\le55$  

• AND

• OR

Open Ended

What would be the first step to isolate the absolute value?

 $9\left|x+4\right|+10\le55$  

Multiple Choice

What would be the next step to isolate the absolute value? $9\left|x+4\right|\le45$  

• Divide by 9

• Add 9

• Subtract 4

• Multiply by 9

Multiple Select

Which two inequalities below would be the next step? Click two below

 $\left|x+4\right|\le5$  

•  $x+4\le-5$ 

•  $x+4\ge5$ 

•  $x+4\le5$ 

•  $x+4\ge-5$ 

Multiple Choice

Solve the absolute value inequality.

 $6\left|x+3\right|-10\ge-4$  

•  $x\le-4\ or\ x\ge-2$  

•  $-4<x<-2$  

•  $-2<x<4$   

•  $x\le-4\ or\ x\ge2$  

Open Ended

Write in your own words the steps to solve absolute value inequalities.