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# Understanding steps when solving equations

Created by Sal Khan.

Video transcript

Create a list of steps, in order, that will solve the following equation... It gives the equation here, and they have a bunch of steps that they want us to put in order. So let's just work it out on this scratchpad. You might be able to work these out in your head eventually... but I'll do it on this scratchpad first. So first I'm just going to solve this the way I might try to solve it. So let's say we have: 5x minus 11 is equal to 42. And as we've seen before, whenever I like to solve something, I like to isolate the variable that I'm trying to solve for. So I want to isolate this 5x on one side, and eventually I'm going to try to get that into being an "x". So the best way to isolate is to get rid of this minus 11. Well, the best way to get rid of this minus 11 on the left hand side... is to add 11 to the left hand side. But I can't just do it only to the left hand side, then these two things won't be equal anymore! In order for them to both be equal... I have to do the same thing to both sides. And then I would be left with... well... negative 11 plus 11 is going to be 0... I'm going to be left with 5x is equal to 53. So what was the first step that I just did? Well, I added 11 to both sides. So this is going to be my first step. Now what do I do to solve this? Well once again, I want this to be in the form of "x=something"... then I know what "x" is! Well, what's the best way to just have an "x" here on the left hand side? Well I could divide 5x by 5... that would give me "x". But once again, if I want these two things to be equal to each other, I have to do the same thing to both sides. So I have to divide 53 by 5 as well. And then I'll be left with: "x" is equal to 53 over 5... and I am done! I have solved for the "x" that satisfies this equation. So what's the next thing that I did? Well, I divided both sides by 5. So this right over here is step 2. I added 11 to both sides, then divide both sides by 5. So let's fill that in. So... I'm going to add 11 to both sides... then I'm just left with 5x is equal to 53. And then I divide both sides by 5. Got it right!