Question

Which of the following equations has the solution set {0}?

Answer 1

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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