anonymous
  • anonymous
What values of x make the two expressions below equal? (2x+1)(x-7)/11(x-7)= 2x+1/11 A. All real numbers B. All real numbers except -1/2 C. All real numbers except 7 D. All real numbers except -1/2 and 7
Mathematics
chestercat
  • chestercat
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DanJS
  • DanJS
missing parenthesis
DanJS
  • DanJS
maybe
anonymous
  • anonymous
The best way to go about this problem is for you to plug in the numbers where stated "except"" to see if they work.

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DanJS
  • DanJS
\[\frac{ (2x+1)(x-7) }{ 11(x-7) }=\frac{ 2x+1 }{ 11 }\] is that it
anonymous
  • anonymous
yes that's what I wrote
anonymous
  • anonymous
If not A, but if they do you'd be picking one of the B to D. Simple right?
DanJS
  • DanJS
group the entire numerator in a bra kets
DanJS
  • DanJS
simplify, (x-7) can cancel in the first, but you must keep in mind that x cant be 7, it will make the original expression undefined
DanJS
  • DanJS
then both are over 11, and you can multiply both sides by 11 to cancel those... left with 2x+1 = 2x+1 , true, all reals
anonymous
  • anonymous
so if you cancel x-7 out, top and bottom you're left with (2x+1)-11 right?
anonymous
  • anonymous
/11
DanJS
  • DanJS
yes, \[\frac{ 2x+1 }{ 11 }= \frac{ 2x+1 }{ 11 }\]
DanJS
  • DanJS
It is like saying, 1 = 1, True statement, any value for x is possible there
DanJS
  • DanJS
remember you canceled out (x-7) in the denominator though, so x-7 can not be zero
anonymous
  • anonymous
same exact thing on both sides except the left one has parentheses
DanJS
  • DanJS
right, if you have the same things on both sides, then the variable can be any real number. Except here it can not be 7 since you cancelled out x-7 in the denominator, you cant have x-7=0 or x=7
DanJS
  • DanJS
zero in the bottom is bad
anonymous
  • anonymous
so it would be all real numbers except 7?
DanJS
  • DanJS
yes
anonymous
  • anonymous
thank you ;)-
anonymous
  • anonymous
:)
DanJS
  • DanJS
i forget what they call those solutions x=7, some term
anonymous
  • anonymous
did not know that myself haha
DanJS
  • DanJS
you can check, put x=7 and see if both sides are the same...
anonymous
  • anonymous
i did
DanJS
  • DanJS
extraneous solutions, just popped into my head, check that definition out if it sounds familiar.

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