If you're going through this entire online
Algebra I course,
Well, WolframAlpha allows you to create
widgets to
share its amazing computational power!
See that ‘WolframAlpha widget’ in the righthand column?
When you press ‘Submit’, a popup window opens;
Have fun playing with the widget!
If you want, copyandpaste absolute value sentences from this page.

WolframAlpha Widget 
Now, let's talk about the concepts involved in solving absolute value equations:
Recall first that normal mathematical conventions dictate
that ‘$\,x = k\ $’
represents an entire class of sentences,
including the members
‘$\,x = 2\ $’,
‘$\,x = 5.7\ $’,
and
‘$\,x = \frac{1}{3}\,$’.
The variable
$\,k\ $ changes from sentence to sentence,
but is constant within a given sentence.
Also recall that ‘$\,x=\pm k\ $’ is a shorthand for ‘$\,x = k\ \text{ or }\ x = k\ $’.
When you see a sentence of the form
$\,x = k\ $, here's what you should do:
Recall that ‘$\,\iff \,$’ is a symbol for ‘is equivalent to’.
The power of the sentencetransforming tool
‘$\,x = k \iff x = \pm k\ $’
goes far beyond solving simple sentences like
$\,x = 5\,$!
Since $\,x\,$ can be any real number,
you should think of
$\,x\,$
as merely representing
the stuff inside the absolute value symbols.
Thus, you could think of rewriting the tool as:
‘$\,\text{stuff} = k \iff \text{stuff} = \pm k\ $’
See how this idea is used in the following examples:
$2  3x = 7$  (original equation) 
$23x = \pm 7$  (check that $\,k\ge 0\,$; use the theorem) 
$23x = 7\ \text{ or }\ 23x = 7$  (expand the plus/minus) 
$3x = 5\ \text{ or }\ 3x = 9$  (subtract $\,2\,$ from both sides of both equations) 
$\displaystyle x = \frac{5}{3}\ \text{ or } x = 3$  (divide both sides of both equations by $\,3\,$) 
$5  23  4x = 7$  (original equation) 
$23  4x = 12$  (subtract $\,5\,$ from both sides) 
$3  4x = 6$  (divide both sides by $\,2\,$) 
$3  4x = \pm 6$  (check that $\,k\ge 0\,$; use the theorem) 
$3  4x = 6\ \text{ or }\ 3  4x = 6$  (expand the plus/minus) 
$4x = 3\ \text{ or }\ 4x = 9$  (subtract $\,3\,$ from both sides of both equations) 
$\displaystyle x = \frac{3}{4}\ \text{ or }\ x = \frac{9}{4}$  (divide both sides of both equations by $\,4\,$) 
Solve the given absolute value equation.
Write the result in the most conventional way.
For more advanced students, a graph is displayed.
For example, the equation $\,2  3x = 7\,$
is optionally accompanied by the
graph of $\,y = 2  3x\,$ (the left side of the equation, dashed green)
and the graph of
$\,y = 7\,$ (the right side of the equation, solid purple).
In this example, you are finding the values of $\,x\,$ where the green
graph intersects the purple graph.
Click the “show/hide graph” button if you prefer not to see the graph.
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
