SOLUTION: question: (! = absolute value bars) !16-3x!=4x-12 i keep getting -4 =x and 28=x but the answer key states just 4?

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 Click here to see ALL problems on absolute-value Question 628344: question: (! = absolute value bars) !16-3x!=4x-12 i keep getting -4 =x and 28=x but the answer key states just 4?Answer by Edwin McCravy(8903)   (Show Source): You can put this solution on YOUR website!```Equations involving absolute values or square roots often have extraneous answers. (Answers that don't check in the original equations, and thus are not solutions). This is such a case. Let's go through the whole thing: |16 - 3x| = 4x - 12 Case 1: when 16-3x equals the value of the right side. 16 - 3x = 4x - 12 -7x = -28 x = 4 Case 2: when 16-3x equals -1 times the value of the right side. 16 - 3x = -(4x - 12) -7x = -4x + 12 -3x = 12 x = -4 You are right except for one thing. You must check absolute value equations for extraneous solutions. If you check x=4, you will find that it is a solution: Checking x = 4, |16-3x| = 4x-12 |16-3(4)| = 4(4)-12 |16 - 12| = 16 - 12 |4| = 4 4 = 4 That checks. So 4 is a solution. But watch what happens when we try checking x = -4 in the original equation: |16-3x| = 4x-12 |16-3(-4)| = 4(-4)-12 |16 + 12| = -16 - 12 |28| = -28 28 = -28 So, as you see that does not check. So -4 must be discarded since it is not a solution. [Incidentally the absolute value bars are on your keyboard, just above the ENTER key and below the Backspace key. Hold down the shift and press the key for the backward slash \. What's printed on the key looks like two small vertical dashes, one above the other, but it types as |. Edwin```