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CCSS.Math:

solve for x and check your solution we have X divided by 3 is equal to 14 so to solve for x to figure out what the variable X must be equal to we really just have to isolate it on the left hand side of this equation it's already sitting there and we have X divided by 3 is equal to 14 we could also write this as 1/3 X is equal to 14 obviously x times 1/3 is going to be x over 3 these are equivalent so how can we just end up with an X on the left hand side of the either of these equations these are really the same thing or another way how can we just have a 1 in front of the X a 1x which is really just saying X over here well I'm dividing it by 3 right now so if I were to multiply both sides of this equation by 3 that would isolate the X and the reason that would work is if I multiply this by 3 over here I'm multiplying by 3 and dividing by 3 that's equivalent you would just that's equivalent to multiplying or dividing by 1 these guys cancel out but remember if you do it to the left hand side you also have to do it to the right hand side and actually I'll do both of these equations at the same time because they're really the exact same equation so what are we going to get over here on the left hand side 3 times anything divided by 3 is going to be that anything we're just going to have an X left over on the left hand side and on the right hand side what's 14 times 3 3 times 10 is 30 3 times 4 is 12 so it's going to be 42 so we get X is equal to 42 and the same thing would happen here 3 times 1/3 is just 1 so you get 1x is equal to 14 times 3 which is 42 now let's just check our answer let's substitute 42 into our original equation so we have 42 in place 4x in place 4 x over 3 is equal to 14 so what's 42 divided by 3 and we could do a little bit of I guess we call it medium long division it's not really long division 3 into 4 3 goes into 4 one time 1 times 3 is 3 you subtract 4 minus 3 is 1 bring down the 2 3 goes into 12 4 times so 3 goes into 14 3 4214 times so this right over here simplifies to 14 and it all checks out so we're done