The correct answer is:
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[A]: " -14m − 7m + 1 = -7m + 1 " .
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Note: All of the answer choices given contain "ONE" variable, "m".
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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 ").
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Specifically, for "Answer choice: [A]:
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-14m − 7m + 1 = -7m + 1 ;
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When we plug in "0" for all values of "m", both sides of the equation are equal:
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-14*(0) − 7*(0) + 1 =? -7*(0) + 1 ?? ;
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0 − 0 + 1 = ? 0 + 1 ?
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1 = 1 ? Yes!
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Let's try Answer choice: [B] ; which is:
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"-14m + 7m + 1 = -7m + 2 " ;
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If we plug in "0" for ALL values of "m" (both sides, of course), does the equation hold true?
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-14*(0) + 7*(0) + 1 = ? -7*(0) + 2 ?? ;
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0 + 0 + 1 = ? 0 + 2 ?? ;
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1 = ? 2 ??? No! 1 ≠ 2 ;
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As such, "Answer choice: [B}" does NOT have the solution set: "{0}" ; and is not the correct answer; (and is not a correct answer).
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Now, let's try the remaining "Answer choice: [C]:"
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14m − 7m − 1 = -7m + 1 ;
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If we plug in "0" for ALL values of "m" (both sides, of course), does the equation hold true?
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14*(0) − 7*(0) − 1 = -7*(0) + 1 ;
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0 − 0 − 1 =? 0 + 1 ?? ;
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- 1 = ? 1 ??? No! -1 ≠ 1 ! ;
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As such, "Answer choice: [C]" does NOT have the solution set: "{0}" ;
and is not the correct answer; (and is not a correct answer).
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The answer is: [A]: " -14m − 7m + 1 = -7m + 1 " .
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