Question 1199825
I need your help desperately.

1. Consider the following equation,
n(7x-3) = 21x+5.
For what value of n will the equation result in no solution?


2. Consider the following equation,

n(3x+2) = -9x-6.
For what value of n will the equation result in infinitely many solutions?
Please, help me with these questions. Explain in detail.
Thank you.
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<pre>
(1)  Equation (1) has no solution if and only if n= 3.


     Indeed, if n= 3, then the equation takes the form

          3*(7x-3) = 21x - 5

     or, equivalently,

          21x - 9 = 21x - 5.


     The last equation, OBVIOUSLY, has no solution;  otherwise, -9 = -5, which is absurd.
</pre>

Part (1) is complete.


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Part &nbsp;(2) &nbsp;is very similar.  &nbsp;&nbsp;Try to solve it on your own.


You may report me your answer for part &nbsp;(2) - I will check it.



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<U>Comment from student</U>: My work for part 2. n(3x + 2) = -9x - 6 3nx + 2n = -9x - 6 


If n = -3, we get the following: -9x - 6 = -9x - 6 So, when n = -3, the equation has an infinite amount of solutions. 


Is this right? I need to know tonight. Thanks.




<U>My response</U>.  &nbsp;&nbsp;Your work is correct.  &nbsp;Everything is &nbsp;&nbsp;RIGHT.


Glad to see your perfect work.



Keep going.



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I also got your another comment, posted before your last comment.


These comments are so different by the tone, that I could not believe 
that they are written by the same person.