Question

Lin was looking at the equation 2x-32+4(3x-2462)=14x.she said”I cant tell right away there are no solutions, because on the left side, you will have 2x+12x and a bunch of constants, but you have just 14x on the right side.” Do you agree with Lin? Explain your reasoning.

Answer 1

Disagree with Lin: There are no solutions because 12x+2x is equal to 14x, if 14x=14x on both sides, the x variable can be cancelled out since they have the same slope

Answer 2

Answer:

Totally disagree with Lin.

When an equation don't have solution, it's because variables are cancelled or eliminated.

In this case, if we operate left side, we will have a term 14x, and the right side of the equation there's also 14x, that means that variable will be eliminated, like this:

$2x-32+4(3x-2462)=14x\\2x-32+12x-9848=14x\\14x-14x=9848+32\\0x=9880\\0=9880$

As you can see, the equation ends in a false result, that means it doesn't have any solution, and we can tell by just seeing the first line of the equation like Lin says.

So, totally disagree with Lin, she can tell from the beginning that the equation doesn't have a solution.