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# Finding mistakes in one-step equations

CCSS.Math:

## Video transcript

Carly tried to solve an equation step by step and they tell us they see we see how she tried to solve the equation they say find Carly's mistake let's see what Carly did so it's she started with seven times a is equal to 28 then on the left hand side she divides it by a and on the right hand side she divides by seven well this seemed strange when you're manipulating the equation whatever you do to one side you have to do to the other side over here she decides to divide the left side by a on the right side she should divide by a as well or if she wants to divide the right side by seven she should divide the left side by seven as well but she's dividing both sides by two different things so step one is where is where she makes the mistake the right thing for her to do or I guess maybe the the most reasonable thing if she wants to solve for a divide both sides by seven then she would have been left with just an A on the left-hand side because it had been 7 a or seven and a four they are interested Oh a must be equal to 4 so let's let's keep going let's do a let's do a few more of these Trent tried to solve an equation step by step all right fine Trent's mistakes a lot of mistakes happening in algebra problems right now so G over 3 is equal to 4 over 3 now let's see the first step G over 3 times 3 so he's multiplying the left hand side times 3 and on the right hand side he's multiplying by 1/3 so once again he's doing two different things to the left and the right hand side even they're supposed to do the same thing if you do two different things the Equality will not hold anymore notice if these two things are if you G over 3 is equal to 4 if you multiply this times 3 and you only multiply this times 1/3 well then this thing is going to become larger because if you multiply by 3 that's going to be larger if you take the same thing and multiply it by 1/3 and then the Equality won't hold true anymore in order for it to hold true if you're gonna multiply the left by 3 have to multiply the right by 3 so he made a mistake on step one all right link tried to solve an equation step by step alright find Ling's mistake let's see 12 is equal to P plus 6 point 2 all right so now it looks like on the tan side Ling adds 6.2 and on the right hand side so there was p+ 6.2 is the old right hand side but it looks like they then try to subtract 6.2 so it's the same number but over here there's adding it and over here they're subtracting it so they're not doing the same thing to both sides if you want to add 6.2 to the left hand side you need to add 6.2 to the right hand side or if you want to subtract 6.2 from the right hand side you have to subtract 6.2 from the left hand side so a lot of mistakes going on in step 1 let me see if I can find one where there's not a mistake in step 1 all right a lot I've tried to solve an equation step by step for C equals 12 divides the left hand side by 4 and then multiplies the right hand side by 4 know if you're going to do divide the left hand side before you have to divide the right hand side by 4 as well you don't multiply by 4 so a mistake in step one let's do one more of these all right n plus 12 is equal to 18 point 3 all right so over here you had n plus 12 and then Reiko subtracts 12 so if you subtract 12 from the left hand side he needs to subtract 12 from the right hand side and it looks like he does that he had 18 point 3 and he subtracts 12 so he subtracts 12 from both sides so the left hand side is now n plus 12 minus 12 it was just N which is why he subtracted 12 so you just left with an N on the left hand side and on the right hand side let's see 18 point 3 minus 12 well 18 minus 12 is 6 so this should be six point three so he made a little bit of an arithmetic mistake in step he made an arithmetic mistake and I think we are all done