What is the solution to –4|–2x + 6| = –24? x = 0x = 0 or x = –6x = 0 or x = 6no solution

Note that  –4|–2x + 6| = –24  can be greatly simplified by dividing both sides by -4:      |-2x+6| = 6.  This, in turn, can be simplified by dividing everything by 2:

|-x+3| = 3.  There are two solutions:

Case 1:  -x+3 is already positive.  The absolute value operator is unneeded.  -x+3 = 3.  Then x = 0.

Case 2: -x+3 is negative.  Then rewrite  |-x+3| = 3 as -(-x+3) = 3.  Solving for x:  x - 3 = 3, and x = 6.  

The solution set is {0, 6}.

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