Absolute Value Equations

A(n) __________________ is an equation that contains absolute value expressions.

• absolute value equation

• linear equation

• quadratic equation

• exponential equation

A(n) _____________________ solution is an apparent solution that must be rejected because it does not satisfy the original equation.

• extraneous

• double

• exponential

• progressive

Tags

CCSS.HSA.REI.A.2

TRUE or FALSE: It is possible for absolute value equations to have two solutions.

• True

• False

 $\left|x\ -\ 1\right|\ =\ 4\$  

• 5 and - 3 

• 4 and - 1 

• 4 and - 4 

• 3 and - 5 

 $\left|-3d\right|\ =\ 15\$  

• 5 and - 5 

• 45 and - 45 

• 12 and - 12 

• 18 and - 18 

 $\left|3x\ +\ 9\right|\ -\ 10\ =\ -4\$  

• - 1 and - 5 

• 1 and 5 

• 14 and 6

• - 14 and - 6 

 $\left|4x\ -\ 4\right|\ =\ -\ 16\$  

• 5 and 3 

• - 5 and - 3 

• no solution 

• infinite solutions 

 $\left|3x\ -\ 4\right|\ =\ \left|3x\ -\ 5\right|\$  

• no solution 

• infinite solutions 

• 1.5 

• 0 

 $\left|2x\ +\ 2\right|\ -\ 9\ =\ -2\$  

Does the equation given have a solution? 

• Yes it will because we have to isolate the absolute value first

• No it will not because the right side is equivalent to a negative number 

 $\left|x\ -\ 4\right|\ =\ p\$  


In the equation above, for any real number p, the equation will ___________________ have two solution(s). 

• always 

• sometimes 

• never