Which of the following equations is NOT equivalent to 4x^2 = z^2 - 9 ?  Choose the correct option.
A) 4x^2 + 9 = z^2 B) 4x^2 - z^2 = -9 C) 4x^2= (z + 3)(z - 3) D) 2x = z - 3 E) x^2 = (z^2-9)/4
4X^2 = z^2 - 9   The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.   Looking at Answer D, we have....   2X = z - 3   While you COULD take the square root of both sides of the original equation, it's important to note that the square root of z^2 - 9 is NOT (z-3).   z^2 - 9 can be factored into (z-3)(z+3), but neither of these parentheses is the square root of z^2 - 9.   You can see the proof when you square either of the two parentheses:   (z-3)^2 = z^2 - 6X + 9   (z+3)^2 = z^2 + 6x + 9   Thus, 2x = z - 3 is NOT equivalent to the prompt.
<result>D</result>
Which of the following equations is NOT equivalent to 4x^2 = z^2 - 9 ?