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Emma substitutes 3 for x in a one-variable linear equation and finds that it makes the equation true. She then substitutes 5 for x in the same linear equation and finds out that 5 also makes the equation true. What can you conclude about the number of solutions of the equation? Explain your reasoning.

Guest Apr 29, 2017
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 #1
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If x can take more than one value, then you may have many, many or perhaps an infinite number of solutions.

Guest Apr 29, 2017
 #2
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Emma substitutes 3 for x in a one-variable linear equation and finds that it makes the equation true. She then substitutes 5 for x in the same linear equation and finds out that 5 also makes the equation true. What can you conclude about the number of solutions of the equation? Explain your reasoning.

 

I think you are correct guest but you have not tried to give a reason.

 

What about if the equation was

(x-3)(x-5)=0      x=3 and x=5 both make it true..

Oh that is no good because f(x)=(x-3)(x+5) is not linear.  

 

I think the eqation is    

mx+b=k  

but m,b and k are all constants.

If this is true for x=5 and x=3 then m must equal 0  and k must equal b

So this must be the formula for a horizonal line.

 

f(x)=k

so any value of x will satisfy it.  There are an infinite number of solutions :)

Melody  Apr 30, 2017

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