What is an absolute value equation that has the solutions X=6 X=18?

or:What is an absolute value equation that has the solutions X=6 X=18?or:I never heard of an \"absolute value equation\". It occurs to me that you mi

or:What is an absolute value equation that has the solutions X=6 X=18?

or:I never heard of an \"absolute value equation\". It occurs to me that you might mean a second power equation, also called \"parabolic curve\".y = (x - 6)(x - 18)Looks like this:www.wolframalpha.com/input/?ab=c&i=plot+y+%3D+(x+-+6)(x+-+18)You can also express that as |y| = (x - 6)(x - 18) to emphasize the \"absolute value\" part. (That makes two curves on the plot.)

or:I've never seen such a question, so let's walk through the steps.First, the absolute function generates two points at any nonzero horizontal crossing (it's shaped like a V), so this should be doable with an internal linear function.Arbitrarily chose x=18 to generate a positive and 6 negative.What happens if we take 0:|ax + b| = 0=> 18 * a + b = 0 ; -(6 * a + b) = 0 => a = 0 ; b = 0Not a very interesting solution.Let's try again with a nonzero constant:|ax + b| = c=> 18 * a + b = c ; -(6 * a + b) = c=> 18a + b = -6a - b => b = -12aThis generates an infinite number of equations defined by this relation - basically, multiply both sides by a constant. Let's pick a = 1 for convenience.a = 1, b = -12, c = 6|x - 12| = 6Testing it out:|6 - 12| = |-6| = 6 ; |18 - 12| = |6| = 6QED

Tags:equations,