Solving absolute value equations and inequalities

Solving absolute value equations and inequalities

Review

Solve the absolute value equations

Multiple Choice

What does absolute value mean?

• Everything is positive

• Everything is negative

• Distance away from zero

Multiple Choice

Solve

 $\left|x+5\right|=8$  

• x=6

• x=3

• x=6 or x=2

• x=3 or x=-13

Multiple Choice

Solve

 $\left|x+7\right|=9$  

• x=2 or x= -16

• x=-16

• x=16 

• x=2

Multiple Choice

Solve

 $\left|x-4\right|=5$  

• x= -4  or  x=4

• x=-1 or x = 9

• x= 6 or x= -6

• x=-4 or x=5

Multiple Choice

Solve

 $\left|\frac{x}{10}\right|=2$  

• x= 12

• x=0  or x=12

• x= -20  or x=20

• x= -8

Multiple Choice

Solve

 $\left|2x+4\right|=8$  

• x= 10 or x=-9

• x=2  or x= -6

• x= -4  or  x=6

• x= -2

Solve absolute value inequalities

Multiple Choice

Solve the absolute value inequality:

 $\left|x+7\right|>10$  

• -17 < x < 3

• x < -17  or  x > 3

• x > 3

• x < -17

Multiple Choice

Solve the absolute value inequality:

 $\left|x+2\right|\ge3$  

•  $x\le-5\ \ or\ \ \ x\ge1$  
  

•  $x\le-5$  
  

•  $x>1$  
  

•  $-5<x<1$  
  

Multiple Choice

Solve the absolute value inequality:

 $\left|x+2\right|>1$  

•  $x\le-1\ \ or\ \ \ x\ge-3$  
  

•  $x\le-5$  
  

•  $x<-3\ \ or\ \ \ x>-1$  
  

•  $-5<x<1$  
  

Multiple Choice

Solve the absolute value inequality:

 $\left|x-7\right|<6$  

•  $-10<x<-4$  
  

•  $-12<x<-2$  
  

•  $1\le x\le13$  
  

•  $1<x<13$  
  

Multiple Choice

Solve the absolute value inequality:

 $\left|x+1\right|<1$  

•  $0<x<2$  
  

•  $-2<x<0$  
  

•  $-2\le x\le0$  
  

Multiple Choice

Solve the absolute value inequality:

 $\left|2x-5\right|<23$  

•  $9<x\le-14$  
  

•  $-14<x<-9$  
  

•  $-9\le x\le14$  
  

Multiple Choice

Select the graph for the following inequality

 $1\le x\le9$  

Multiple Choice

Select the graph for the following inequality

 $x<-6\ \ \ or\ \ \ x>2$