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### Course: 6th grade > Unit 7

Lesson 5: Finding mistakes in one-step equations# Finding mistakes in one-step equations

In this lesson, we learned how to spot mistakes in solving algebraic equations. We saw that it's crucial to apply the same operation to both sides of the equation. We also learned the importance of accurate arithmetic in getting the correct answer. Lastly, we saw that not all steps, even if algebraically correct, help simplify the equation.

## Want to join the conversation?

- Question. Why would it matter if you got step one wrong if you got step 2 right?(13 votes)
- I guess it's because teachers want us to do everything right the first time, and while you may get lucky to get the correct answer, in the end, it's the work that mainly counts and you may not get lucky every time on step two. :/(16 votes)

- Why are almost all the mess ups on step one?(6 votes)
- I don't know. Maybe it is because you are most likely to mess up on step one?? I don't really know, this is just a guess.(5 votes)

- on 2.35 why are we flipping the fractions.(5 votes)
- because it makes it equivalent to 1 and cancels out the fraction and changes the other one.(4 votes)

- y + 5 = 12

y + 5 - 5 = 12 - 5

y = 7

Is this correct? Why or why not?(4 votes) - 1/3 = 2/3x

3/2 * 1/3 = 3/2 * 2/3x

1/2 = x

Is that correct? Why or why not?(3 votes)- Yes that is correct, if you multiply numerators and denominators, you get 3/6 which reduces to 1/2.(2 votes)

- where do we use equations in everyday life?(2 votes)
- On the 2nd problem, you said that whatever you do to the right/left hand side, you do to the left/right hand side, but instead of multiplying by 1/3, couldn't you just divide by 1/3 instead? Any thoughts?(2 votes)
- I'm a little confused as to what you mean, but if I gather correctly you are referring to dividing g/3 = 4/3?(1 vote)

- its more than one step so why do they say that(2 votes)
- Lisa would be right(1 vote)
- theres is 2 question needs to be FIXED!(0 votes)

## Video transcript

- [Instructor] We're told that Lisa tried to solve an equation. See, 42 is equal to 6a, or six times a. And then we can see her steps here. And they say, where did
Lisa make her first mistake? So pause this video, and see
if you can figure that out. And it might be possible
she made no mistakes. All right. Well, we know she ends
up with seven equals six, which is sketchy, so let's
see what happened here. So right over here, it looks like, well, she did something
a little bit strange. She divided the left-hand side by six, and the right hand side by a. You don't want to divide
two sides of an equation by two different things. Then it's no longer
going to be an equation. The equality won't hold. An algebraically legitimate thing is to do the same thing to both sides, but she didn't do it here. So this is where she
made her first mistake. Let's give another example here. So here it says that Jin
tried to solve an equation. All right, x plus 4.7 is equal to 11.2. Where did Jin make his first mistake? Pause this video, and
try to figure it out. All right, so it looks like in order to isolate the x on the left-hand side, Jin is
subtracting 4.7 from the left, and then also subtracting
4.7 from the right. So that is looking good, doing
the same thing to both sides, subtracting 4.7 from both sides. And then over here on the left-hand side, these two would cancel. So you'd be left with just an x, and let's see, 11.2 minus 4.7. 11.2 minus four would be 7.2, and then minus the 0.7 would be 6.5. So this is where Jin made his mistake, on the calculating part. Let's do another example,
this is a lot of fun. So here we are told that Marina
tried to solve an equation, and we need to figure out where Marina made her first mistake. All right, one-sixth is
equal to two-thirds, why? So the first step, or the first thing that
Marina did right over here is to multiply both sides of this equation by the reciprocal of two-thirds,
which is three halves. Multiplied the left-hand
side by three halves, multiplied the right-hand
side by three halves, which is a very reasonable thing to do. We're doing the same thing to both sides, multiplying by three halves. And then when we go over here, let's see, three halves times one-sixth. We could divide the numerator
and the denominator by three. So it's gonna be one over two. So that indeed is going to
be one half times one half, which is one-fourth, so that checks out. And on this side, if you multiply three
halves times two-thirds, that's going to be one,
so this checks out. So it actually looks like
Marina did everything correctly. So no mistake, no mistake for Marina. Let's do one last example. So here, Taylor is trying
to solve an equation. And so where did Taylor
first get tripped up? N minus 2.7 is equal to 6.7. In order to isolate this N over here, I would add 2.7 to both sides, but that's not what Taylor did. Taylor subtracted 2.7 from both sides. So the first place that
Taylor starts to trip up, or move in the wrong
direction is right over here. Now, what Taylor did is not
algebraically incorrect. You would end up with n
minus 5.4 is equal to four, but it's not going to help
you solve this equation. You just replaced this equation with another equivalent equation that is no simpler than the one before. And then of course, instead of getting n
minus 5.4 equals four, Taylor calculated incorrectly as well. But where they first
started to get tripped up, or at least not move
in the right direction would be right over here.