Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12? x = –2, x = –4 x = –2, x = 4 x = 2, x = –4 x = 2, x = 4

The correct answer is:  [C]:  " x = 2,  x = - 4 " .
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 Explanation:
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Given the function: " f(x) = –5|x + 1| + 3 " ;  

        for what values of "x" is:  " f(x) = -12 " ?
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Replace the "f(x)" notation with "-12" ; 

    -12  = –5|x + 1| + 3 ;

↔  –5|x + 1| + 3 = -12 ; 

and solve for "x" ; {the values for "x"} ;
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We have: 
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       -5|x + 1| + 3 = -12 ;

Subtract "3" from EACH SIDE of the equation:

       -5|x + 1| + 3 − 3 = -12 − 3 ; 

to get: 

          -5|x + 1|  = -15

Now, divide EACH SIDE of the equation by "-5" ; 

          {-5|x + 1| } / -5 = -15 / -5 ;

to get:

              |x + 1| = 3 .
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To solve for "x" ; 
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We have 2 (two values).  Let us set up "Case 1" and "Case 2" scenarios:
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Case 1)  
 
   " x + 1 = 3 "  ;

Subtract:  "1" from each side of the equation; 

     x + 1 − 1 = 3 − 1 ;

to get:

            x = 2 ;   {So, we know that our answer is going to be:
                           "Answer choice:  [C] or [D]" ; since these are the only answer                                choices given that contain a solution of "x = 2" .
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Case 2)
 
      " - (x + 1) = 3 "  ;

→  " -1(x + 1) = 3 ; 

Divide each side of the equation by "-1" ; as follows:

→    {-1(x + 1) } / -1 = 3 / -1 ; 

to get:

     →  x + 1 = -3 ;

Subtract "1" from each side of the equation: 

     →  x + 1 − 1  = -3 − 1 

to get:

     →     x = - 4  .
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So:  x = 2 and -4 ;  which is:  Answer choice:  [C]:  " x = 2,  x = - 4 " .
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