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# Creating an equation with no solutions

## Video transcript

whereas to use the dropdowns to form a linear equation with no solutions so no solution linear equation with no solutions is going to be one where I don't care how you manipulate it the thing on the Left can never be equal to the thing on the right and so let's see what options they give us so one they want us to we can pick the coefficient on the x-term and then we can pick the constant so if we made this negative 11x so now we have a negative 11x on both sides here on the left hand side we have negative 11x plus 4 if we do something other than 4 here so if we didn't like say negative 11x minus 11 then here we're not going to have any solutions and you're saying hey Sal how did you come up with that well think about it right over here we have a negative 11x here we have a negative 11x there if you wanted to solve it algebraically you could add 11 X to both sides and both of these terms would cancel out with each other and all you would be left with is a 4 is equal to a negative 11 which is not possible for any X that you pick another way that you think about it is here we have negative 11 x is not some number and we're adding 4 to it and here we're taking negative 11 times that same number and we're subtracting 11 from it so if you take a negative 11 times some number on one side you add 4 and on the other side you subtract 11 there's no way it doesn't matter what X you pick there's there's no X for which that is going to be true but let's check our answer right over here