SOLUTION: I know the answer is 7 but how would you show the work for this question: For what value of a is a(x-5)=9x-25-2x-10 an identity?

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Question 217280: I know the answer is 7 but how would you show the work for this question: For what value of a is a(x-5)=9x-25-2x-10 an identity?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are two ways to do this, here's one way:


a%28x-5%29=9x-25-2x-10 Start with the given equation.


a%28x-5%29=7x-35 Combine like terms.


a%28x-5%29=7%28x-5%29 Factor out the GCF 7 from the right side.


Divide both sides by x-5.


a=7 Simplify


So the value a=7 makes a%28x-5%29=9x-25-2x-10 an identity. Go ahead and try to solve 7%28x-5%29=9x-25-2x-10 to confirm the answer.