Main content

# Finding mistakes in one-step equations

CCSS Math: 6.EE.B.7

## Video transcript

- [Voiceover] 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. So let's see what Carly did. She started with 7a = 28. Then on the left hand side she divides it by a and on the right hand side she divides by 7. Well this seems strange. When you're manipulating an 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 7, she should divide the left side by 7 as well, but she's dividing both sides by two different things. So step 1 is where she makes the mistake. The right thing for her to do, or I guess maybe the most reasonable thing, if she wants to solve for a, divide both sides by 7. Then she would have been left with just an a on the left hand side, because it would have been 7a/7 and a 4 over there. She would have said, oh, a must be equal to 4. So let's keep going. Let's do a few more of these. Trent tried to solve an equation step by step. All right. Find Trent's mistake. So a lot of mistakes happening in algebra problems right now. So g/3 = 4/3. Now let's see. The first step. g/3 x 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 though you'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 g/3 = 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 is you multiply by 3 that's going to be larger if you take the same thing and multiply it by 1/3. Then the equality won't hold true anymore. In order for it to hold true, if you're going to multiply the left by 3 you have to multiply the right by 3. So he made a mistake on step 1. All right. Ling tried to solve an equation step by step. All right. Find Ling's mistake. Let's see 12 = p + 6.2. All right. So now it looks like, on the left hand 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 they then try to subtract 6.2. So it's the same number, but over here they're 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. 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 one where there's not a mistake in step 1. All right. Alanna tried to solve an equation step by step. 4c = 12, divides the left hand side by 4 and then multiplies the right hand side by 4. No if you're going to divide the left hand side by 4 you have to divide the right hand side by 4 as well. You don't multiply it by 4. So a mistake in step 1. Let's do one more of these. All right. n + 12 = 18.3. So over here you had n + 12 and then Rico subtracts 12. So if he subtracts 12 from the left hand side he needs to subtract 12 from the right hand side. It looks like he does that. He had 18.3 and he subtracts 12. So he subtracts 12 from both sides. So the left side is now n + 12 - 12, was just n, which is why he subtracted 12, so you're just left with an n on the left hand side, and on the right hand side, let's see, 18.3 -12. Well 18 - 12 is 6, so this should be 6.3. So he made a little bit of an arithmetic mistake in step, he made an arithmetic mistake and I think we are all done.