Absolute Value Equations and Inequalities

Solve:

 $\left|x-2\right|=3$  

• x = 5 or x = -5

• x = 5 or x = -1

• x = 5 or x = 1

• x = -5 or x = -1

Solve:

 $\left|2x-1\right|=5$  

• x = -2 or x = 3

• x = 2 or x = -3

• x = -2 or x = -3

• x = -1 or x = 3

Solve:

 $\left|5x+10\right|=30$  

• x = 4 and x = -8

• x = 4 or x = -8

• x = 7 or x = -8

• x = 7 and x = -8

Solve:

 $\left|x+4\right|>7$  

• x < -11 or  x > 3 

• -11 < x < 3

• x > -11 or x > 3

• x < -11 or x > -3

 $\left|2x-3\right|\le9$  

•  $-3\le x\le6$  

•  $3\le x\le-6$  

•  $x\ \le\ 6\ or\ x\ \ge-3$  

•  $-6\le x\le6$  

Solve:

 $\left|3x+6\right|>15$  

•  $x\ <\ -7\ or\ x\ >\ 3$  

•  $x<7\ or\ x\ >-\ 3$  

•  $x<-7\ or\ x>-3$  

•  $x<7\ or\ x\ >3$  

Solve:

 $\left|3x+2\right|-1\le9$  

•  $-4\le x\le\frac{8}{3}$  

•  $-4\ge x\le\frac{8}{3}$  

•  $-4\le x\le8$  

•  $4\le x\le\frac{8}{3}$  

Solve:

 $\left|x-4\right|+5>7$  

•  $x<2\ or\ x>6$  

•  $x<-2\ or\ x>6$  

•  $x>2\ or\ x\ <6$  

•  $x<2\ or\ x>4$