The correct answer is: _________________________________________________________ [A]: " -14m − 7m + 1 = -7m + 1 " . _________________________________________________________ Note: All of the answer choices given contain "ONE" variable, "m". __________________________________________________________ Among the all the answer choices given (that is, among all the 3 (THREE) answer choices given), this answer choice: "{A}", is the only one which holds true; (that is, maintains a true equation— both sides of the equation are equal—, when "m = 0 "). __________________________________________________________ Specifically, for "Answer choice: [A]: ____________________________________________ -14m − 7m + 1 = -7m + 1 ; ____________________________________________ When we plug in "0" for all values of "m", both sides of the equation are equal: ____________________________________________ -14*(0) − 7*(0) + 1 =? -7*(0) + 1 ?? ; __________________________________________________ 0 − 0 + 1 = ? 0 + 1 ? __________________________________________________ 1 = 1 ? Yes! ___________________________________________________ Let's try Answer choice: [B] ; which is: ___________________________________________________ "-14m + 7m + 1 = -7m + 2 " ; ________________________________________________________ If we plug in "0" for ALL values of "m" (both sides, of course), does the equation hold true? _______________________________________________________ -14*(0) + 7*(0) + 1 = ? -7*(0) + 2 ?? ; _______________________________________________________ 0 + 0 + 1 = ? 0 + 2 ?? ; _______________________________________________________ 1 = ? 2 ??? No! 1 <span>≠ 2 ; _______________________________________________________ As such, "Answer choice: [B}" does NOT have the solution set: "{0}" ; and is not the correct answer; (and is not a correct answer). ________________________________________________________ Now, let's try the remaining "Answer choice: [C]:" ________________________________________________________ 14m − 7m − 1 = -7m + 1 ; _______________________________________________________ </span> If we plug in "0" for ALL values of "m" (both sides, of course), does the equation hold true? ________________________________________________________ 14*(0) − 7*(0) − 1 = -7*(0) + 1 ; ________________________________________________________ 0 − 0 − 1 =? 0 + 1 ?? ; ________________________________________________________ - 1 = ? 1 ??? No! -1 ≠ 1 ! ; ________________________________________________________ As such, "Answer choice: [C]" does NOT have the solution set: "{0}" ; and is not the correct answer; (and is not a correct answer). _________________________________________________________ The answer is: [A]: " -14m − 7m + 1 = -7m + 1 " . _________________________________________________________
