SOLUTION: 6!2x + 5!=6x + 24 !=Absolute Value Sign

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Question 158106This question is from textbook Prentice Hall Mathematics Algebra 2
: 6!2x + 5!=6x + 24
!=Absolute Value Sign
This question is from textbook Prentice Hall Mathematics Algebra 2

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


What is between the absolute value bars,
, can either be negative or 
non-negative, so we must always make two 
separate equations, one for each case:

Case 1:   


Then  is non-negative and
we can just replace the absolute value bars
by parentheses, so



becomes simply:






Case 2:   


Then  is negative and so we
must multiply what is between the absolute
value bars by -1 to make it a positive
number, so w replace  by
.  So



becomes 






But we must check both solutions because
sometimes we get extraneous solutions,
that is, bogus solutions, that do not check,
and these must be discarded.

Checking  in original:








So  is a solution.

Checking  in original:








So  is also a solution.

The solutions are -1 and -3.

Edwin

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