#1.4 Solving Absolute Value Equations

Solve for x:
 $\left|x+6\right|=11$  

•  $x=-6\ \ \ \ OR\ \ \ \ x\ =\ 11$ 

• No Solution

•  $x=5\ \ \ \ \ OR\ \ \ \ \ x=-17$ 

•  $x=-5\ \ \ \ OR\ \ \ \ \ x\ =\ 17$ 

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:

 $\left|2x-1\right|=-4$  

•  $x=\frac{1}{2}\ \ \ \ OR\ \ x\ =\ -4$  

• No Solution

•  $x=-\frac{3}{2}\ \ OR\ \ x\ =\ \frac{5}{2}$  

•  $x=\frac{5}{2}\ \ OR\ \ x\ =\ -\frac{3}{2}$  

Tags

CCSS.HSA.REI.B.3

Solve for x:

 $\left|3x-6\right|-9=-3$  

• No Solution

•  $x=0$      OR     $x=4$  

•  $x=2$     OR    $x=-2$  

•  $x=-4$  OR   $x=4$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

 $\left|x\right|=5$  Solve for x:

•  $x=5\ \ \ OR\ \ \ x\ =\ -5$  

•  $x=5$  

•  $x=-5$  

• No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:
 $\left|x-12\right|-3=11$  

•  $x=-2\ \ \ OR\ \ \ x=-26$  
  

•  $x=-2\ \ \ OR\ \ \ x\ =\ 26$  
  

•  $x=3\ \ \ OR\ \ \ x\ =\ 25$  

•  $x\ =\ 4\ \ \ OR\ \ \ x\ =\ -7$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve for x:

 $-2\left|5x-1\right|-3=-11$  

•  $x=-\frac{3}{5}\ \ \ OR\ \ \ x\ =\ 1$  

•  $x=\frac{3}{5}\ \ OR\ \ x\ =\ -1$  

•  $x=-\frac{2}{3}\ \ OR\ \ x\ =\ 5$  

•  $x=\frac{2}{3}\ \ \ OR\ \ \ x\ =\ -5$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:

 $4\left|2x+7\right|=16$  

•  $x=-5.5\ \ \ OR\ \ x\ =\ -1.5$  

•  $x=5.5\ \ \ OR\ \ \ x\ =\ 1.5$  

•  $x=2.4\ \ \ OR\ \ x\ =\ -0.4$  

•  $x=-2.4\ \ \ OR\ \ \ x\ =\ 0.4$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

On a soundtrack the minimum length of a song is 3 minutes and the maximum length is 5 minutes. Write an absolute value equation that represents this minimum and maximum.

• $\left|x-4\right|=1$

• $\left|x-1\right|=4$

• $\left|x-3\right|=5$

• $\left|x-5\right|=3$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve for x:

 $\left|x+3\right|=-2$  

• No Solution

•  $x=5\ \ \ OR\ \ \ x\ =\ -3$  

•  $x=-5\ \ \ OR\ \ \ x\ =\ 3$  

•  $x=-5\ \ \ OR\ \ \ x\ =\ -3$  

Solve for x:

 $\left|-3x\right|=15$  

•  $x=-5\ \ \ OR\ \ \ x\ =\ 5$  

• No Solution

•  $x=-12\ \ \ OR\ \ \ x\ =\ 12$  

•  $x\ =\ 8\ \ \ OR\ \ x\ =\ -8$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3