|x+3| – |4-x| = |9+x| How many solutions will this equation have?	Choose the correct option
A) 0
B) 1
C) 2
D) 3
E) 4
You have |x+3| - |4-x| = |8+x|   First, look at the three values independently of their absolute value sign, in other words:   |x+3| - |4-x| = |8+x|   (x+3) - (4-x) = (8+x)   Now, you're looking at x &lt; - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.   when x=-10   I.) (x+3)   (-10+3)   (-7)   II.) (4-x)   (4-[-10]) (double negative, so it becomes positive)   (4+10)   (14)   III.) (8+x)   (8+-10)   (-2)   In other words, when x &lt; -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.   Here is how I do it step by step.   I.) |x+3| - |4-x| = |8+x|   II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:   (x+3)   x=-3   (-3+3)= 
<gadget id="calculator">(-3+3)</gadget>
<output>0</output>
0   (4-x)   x=4   (4-4)= 
<gadget id="calculator">(4-4)</gadget>
<output>0</output>
0   (8+x)   x=-8   (8+-8) = 1   1
<result>B</result>
|x+3| – |4-x| = |9+x| How many solutions will this equation have?