Testing solutions to equations

so we've got an equation here it says five times X minus three is equal to four times X plus three so what we want to do is we want to figure out an X that satisfies it so there's some number that if I take five multiply it by that number subtract three from it now that's going to be the same thing as if I take four times that number and add three to it and before we go into how to solve these types of things let's just first see if we can test whether something does satisfy this equation and so I have three options here I have X could be equal to five X could be equal to 6 and X could be equal to seven and your goal is to pause this video and figure out which of these X's satisfy this equation which of these values would make this equation be true so I have as I'm assuming that you have tried that so let's work through each of them step one by one so let's say this first one if X is equal to five then in order for this to be true five times five right five times X so five times five minus three needs to be equal to four times everywhere we see an X we're going to put a five there four times actually let me do it this way let me just to color code it so this is the same thing as saying five times five times five minus three let me do that in that same color minus three needs to be equal to four times five four times five plus three plus three color changing is hard plus three now is this true let's see five times five is 25 this is going to be 25 minus three needs to be equal to 20 plus three twenty five minus three is twenty two needs to be equal to 23 no this is not true so X does not equal 5 so this is this is not a solution let's try x equals six so once again we're going to 5 five times our X which is going to be 6x let me just write about minus 3 equal needs to be equal to 4 times our X plus 3 in this case our X is 6 so it's going to be 5 times 6 minus three needs to be equal to 4 times 6 plus 3 what's 5 times 6 what's 30 minus three needs to be equal to 4 times 6 is 24 and then plus 3 well this is true 30 minus 3 is 27 which is indeed equal to 24 plus 3 it's equal to 27 so x equals 6 does satisfy our equation it is a solution and actually as you will see in the future the solution to this equation right over here x equals 6 satisfies this now just for good measure let's just verify that x equals 7 will not will not satisfy it so let me move this up a little bit so if X is equal to 7 we're going to get five times seven minus three needs to be equal to 4 times 7 plus 3 and so we're going to get and all of these cases we do the multiplication first order of operations and it's very clear when you see it kind of in the algebraic notation up here so we're going to do 35 minus three needs to be equal to 28 plus 3 35 minus 3 is 32 28 plus 3 is 31 these do not equal each other so this is not a solution to our original equation