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Question 489034: 9x + 3 = 9x + b
For what value(s) of b does the equation have no solution?
the answer i thought was 3 but than i seen that if i put 3 it would be infienetly solution than i thought it was two but that was incorrect also
Found 2 solutions by Theo, chessace:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is:
9x + 3 = 9x + b
subtract 9x from both sides of this equation to get:
b = 3
in order for this equation to have a solution, the value of b has to be equal to 3.
any other value of b will result in no solution.
if you set b equal to 3, the equation reduces to 3 = 3 which is true, confirming the value of 3 for b is a solution.
if you set b to any other value, like 2, the equation reduces to 3 = 2 which is false, confirming the value of 2 for b is not a solution.
try any value for b other than 3 and you will see that the equation does not have a solution.
the fact that you have 9x + 3 = 9x + b should be your clue that b has to be equal to 3.
the 9x terms will always be equal regardless of the value of x.
that means the other term in each expression has to also be equal.
that can only happen when b = 3.
Answer by chessace(471)  (Show Source):
You can put this solution on YOUR website! You were close. 3 does have infinitely many solutions, but you were not asked to find them (it would take a while!).
"2 is incorrect" is the same as "b=2 make the equation invalid" which implies that "b=2 has no solution", so 2 is a legit value as requested.
In fact, everything but 3 has this property so the answer is b not = 3.
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