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# Creating an equation with infinitely many solutions

## Video transcript

we're asked to use the drop-down to form a linear equation with infinitely many solutions so it's an equation with infinitely many solutions essentially has the same thing on both sides no matter what X you pick so first out my brain just wants to simplify this left hand side a little bit and then think about how I can engineer the right hand side so it's going to be the same as the left no matter what X I pick so right over here if I distribute the 4 over X minus 2 I get 4x minus 8 and then I'm adding X to that and that's of course going to be equal to 5x plus blank and I get to pick what my blank is and so 4x plus X is 5x 5x and of course we still have our minus 8 and that's going to be equal to 5x plus blank so what could we make that blank so this is true for any any X we pick well over here we have 5 times then X minus 8 well if we if we make this a minus 8 or if we subtract 80 or if we make this a negative 8 this is going to be true for any X so if we make this a negative 8 this is going to be true for any X you pick you take give me any X you multiply it by 5 and subtract 8 that's of course going to be that same X multiplied by 5 and subtracting 8 and if you were to try to somehow solve this equation subtract 5x from both sides you would get negative 8 is equal to negative 8 which is absolutely true for absolutely any X that you pick so let's go let me actually fill this in on the exercise so I want to make 5 I wanted it's going to be 5x plus negative 8