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what I want to do in this video is get some practice building an important skill being able to look at some algebra that has happened and see whether it is correct and this is valuable you might look at other people's work you might look at your own work and be able to tell well hey did I do that right and where did I the logic maybe broke down or why am I not getting the answer that I think I should get so let's let's get some practice here so I have an equation 9 x - 9 x and then parenthesis 2x plus 1/3 is equal to 39 and then someone has worked it out this is step one step two and step three they get to the solution x equals two what I want you to do is pause this video and figure out is this solution correct did all the steps they do they make logical sense do they make algebraic sense or did they make a mistake in one of these steps and if so which of these steps did they make a mistake in alright so let's just work through this problem and see if all of these steps are reasonable so in this first step they went from let's see they got an 18 X here so it looks like they distributed the 9 so 9 times 2x would be 18 X and then of course you would also have to do nine times one-third nine times one third would be nine thirds or three so that seems reasonable and you still have a 39 here on the right hand side so step one checks out now let's see what do they do over here over on step after step one or at this stage you had 18x plus three and then over here you only have 18x so they must have they must have subtracted 3 from the left hand side to get rid of this 3 so they subtracted 3 from the left hand side well they subtract 3 from the left hand side they also need to subtract 3 from the right hand side and it looks like they did 39 minus 3 is 36 so that step checks out and so you have 18x is equal to 36 and so to solve for X you just want to divide both sides by 18 so you would get X is equal to 36 over 18 or 2 so all of these steps check out and so this is there there's no no problem here no mistake and you can verify that X and does indeed X does indeed equal 2 let's do let's do some more questions or see if can identify more errors or maybe no errors all right we have 8/3 is equal to three times c plus 5/3 and we want to solve for c pause the video and see if there any of these mistakes are or if any of these steps are incorrect or maybe there's no mistake at all all right let's go step by step so in step one kept the left-hand side the same the right-hand side let's see you go from three times this to 3c so it looks like they're distributing the 3 so 3 times C is indeed 3c and then you want to distribute 3 times 5/3 well it's going to be 5 that's not going to be 5/3 this thing right over here this thing needs to be 5 not 5/3 so that is not correct so step one is where we have the problem let's keep going so let's do one more of these I find this strangely entertaining all right this is a little bit simpler 1/4 are plus two is equal to ten and then they immediately go from that to just 1/4 R so they got rid of this 2 on the left hand side well to do that you could subtract 2 from the left but of course you would also have to do that from the right hand side and so you get 1/4 R plus 2 minus 2 that would just be 1/4 R so that the left hand side makes sense 10 minus 2 is not 12 10 minus 2 is 8 this right over here should be 8 they added 2 on the right hand side they subtracted 2 on the left hand side and they added 2 on the right hand side then the Equality wouldn't hold anymore so you definitely have an error step one is not correct