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## Algebra (all content)

# Describing steps when solving equations

Sal lists the steps necessary in order to solve a linear equation. This is useful for thinking more strategically about equations. Created by Sal Khan.

## Video transcript

Voiceover:Create a list
of steps, in order, that will solve the following equation. It gives the equation here then they have a bunch of steps that they want us to put in order. Let's just work it out
on this scratch pad. You might be able to work this out in your head eventually but I'll do it on this scratch pad first. First, I'm just going to solve this the way that I might try to solve it. 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. I want to isolate this 5x on one side and then eventually I'm
going to try to get that to being an x. The best way to isolate it is to get rid of this minus 11. The best way to get this minus, get rid of that 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. Then I would be left with
well, negative 11 plus 11 is going to be zero. I'm going to be left
with 5x is equal to 53. 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. Once again I want this to be on the form of x equals something that I know what x is. What's the best way to just have an x here on the left hand side? I could divide 5x by five that would give me x. Once again if I want these two things to be equal to each other, I have to do the same thing to both sides. I have to divide 53 by five as well and then I'll be left with, I'll be left with x is
equal to 53 over five and I am done. I have solved for the x that
satisfies this equation. What's the next thing that I did? I divided both sides by five, so this right over here is step two. I added 11 to both sides then divide both sides by five. Let's fill that in. I'm going to add 11 to both sides, adding 11 to both sides then I'm just left with 5x is equal to 53 and then I divide both sides by five. Got it right.