Equations with variables on both sides: 20-7x=6x-6

we have the equation 20 minus 7 times X is equal to 6 times X minus 6 and we need to solve for X so the way I like to do these is we just like to separate the constant terms which are the 20 and the negative 6 on one side of the equation I'll put them on the right-hand side and then we'll put all of the X terms the negative 7x and the 6x we'll put it all on the left-hand side so to get the 20 out of the way from the left-hand side let's subtract it let's subtract it from the left-hand side but this is an equation anything you do to the left-hand side you also to do the right-hand side if that is equal to that in order for them to still be equal anything I do to the left-hand side I have to do the right-hand side so I subtracted 20 from the left let me also subtract 20 from the right and so the left-hand side of the equation 20 minus 20 is just zero that was the whole point they cancel out don't have to write it down and then I have a negative 7x just cat gets carried down negative 7x and then that is equal to the right-hand side of the equation I have a 6x I'm not adding or subtracting anything to that but then I have a negative 6 minus 20 so if I'm if I'm already six below zero on the number line and I go another 20 below that that's it negative 26 negative 26 now the next thing we want to do is we want to get all of the X terms on the left hand side so we don't want this 6x here so maybe we subtract 6x from both sides so let's subtract 6x from the right subtract 6x from the left and what do we get what do we get the left-hand side negative 7x minus 6x that's negative 13 X right negative 7 of something minus another 6 of that something is going to be negative 13 of that something and that is going to be equal to 6x minus 6x that cancels out that was the whole point a bynes subtracting negative 6x and then we have just a negative 26 or minus 26 depending how you want to view it so just negative 13 X is equal to negative 26 now our whole goal just to remember is to isolate the X and we have a negative 13 times the X here so the best way to isolate it is if we have something times X if we divide by that something will isolate the X so let's divide let's divide by negative 13 now you know by now anything you do the left-hand side of an equation you have to do to the right-hand side so we're gonna have to divide both sides of the equation by negative 13 now what does the left-hand side become negative 13 times X divided by negative 13 that's just going to be X you multiply something times X divided by the something is just going to be you're just going to be left with an X so the left-hand side just becomes an X X is equal to negative 26 divided by negative 13 well that's just positive 2 right a negative divided by negative is a positive 26 divided by 13 is 2 and that is our answer that is our answer now let's verify that it really works that's the fun thing about algebra you can always make sure that you got the right answer so let's substitute it back into the original equation so we have 20 minus 7 times X X is 2 minus 7 times 2 is equal to is equal to 6 times X we've solved for X it is 2 minus 6 minus 6 so let's verify that this left-hand side really does equal this right hand side so the left-hand side simplifies to 20 minus 7 times 2 which is 14 20 minus 14 is 6 that's what the left-hand side simplifies to the right-hand side we have 6 times 2 which is 12 minus 6 12 minus 6 is 6 so they are indeed equal and we did indeed get the right answer