SOLUTION: A. Does the following equation have one solution, two solutions or no solutions? Explain. (absolute value sign) x=3 (absolute value sign) +14=10

You made a typo, the = is either supposed to be a + or a -. I can't
tell which.  But it doesn't matter in this one particular case:



add  to both sides to isolate the absolute value term:



This can have no solution simply by inspection,
because no absolute value can ever be negative, so
the left side, which is an absolute value, could
never equal to the right side, because it is
negative. 

Isolate the absolute value term by adding 6 to both sides:



Remove the parentheses inside the absolute value bars:



Rule for removing absolute value bars in an equation:

 becomes two equations:
, , when N is non-negative:
(There is no solution when  is negative!)

So,  becomes:

 and 



So there are two solutions, -8 and 12, answer (a).

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Divide both sides by -2 to isolate the absolute value.
Notice that when we divide both sides by a negative
numbers, we must REVERSE the inequality symbol!



The rule for removing absolute value bars when the inequality is <:
 where N is positive becomes


So


becomes

 

Add 3 to all three sides to get x in the middle:



, choice (d).

Edwin