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## Algebra (all content)

### Course: Algebra (all content)>Unit 2

Lesson 5: Two-steps equations intro

# 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.

## Want to join the conversation?

• Ok so, I'm in 8th grade and I'm a bad test taker so now im in 7th grade math when i should be in Algebra 1. If I finish this website and write down all my work and show to the counselor, do you think they will let my into a normal class next year? • Showing proof of work completed is not sufficient for an automatic pass, HOWEVER, showing proof of work completed will go a long way in support of your case to ask to write a placement exam. If you really did the work, you should have the ability, and should pass the test.
Do it!
• Can you do the 2 cards he chose in the reverse order? • solve the equation s+j=a for j • Are there any other examples for this? I'm trying to get through algebra and this isn't helping some of the equations this is supposed to help with. • Why in an equation like: 7(x+3)-9 = 5 you get rid of the 7 first, but in an equation like 1/2(x+4)=3 =18 you get rid of the four in the parenthesis first? I thought in the order of operations you multiply or divide BEFORE you add or subtract? Is there any specific rule where you do not follow order of operations.....please HELP!
(1 vote) • First, please understand the the order of operations is a temporarily used tool to guide students until they master the rules for algebraic operations. There are ways to work around that order, if you know the properties of algebraic operations.

For problems like these, you will be isolating the variable. There are often a number of ways of doing that. But the main thing to keep certain about is that you MUST ALWAYS do exactly the same thing to both sides of the equation.
Let me show you more than one way to solve 7(x+3) - 9 = 5, so you can get an idea of what I am talking about:
Method 1:
`7(x+3)-9 = 5` ← divide both sides by 7 (remember you must divide the 9 by 7 as well
`(x+3) - ⁹⁄₇ = ⁵⁄₇` ← now let us add +⁹⁄₇ to both sides
`x+3 = ⁹⁄₇ + ⁵⁄₇` ← now add the fractions
`x+3 = 2` ← now subtract 3
`x = -1`
While that method worked, it involved some fractions, let us try a different approach
Method 2:
`7(x+3)-9 = 5` ← apply the distributive property
`7x+21-9 = 5` ← now combine like terms (that is, 21 - 9)
`7x + 12 = 5` ← now subtract 12 from both sides
`7x = −7` ← now divide by 7
`x = -1`
Well that worked fairly easily, but it isn't always going to be so easy, so let us try one last way (this is the way you are probably being taught in class)
Method 3:
`7(x+3)-9 = 5` ← add 9 to both sides
`7(x+3) = 14` ← divide by 7
`x+3 = 2` ← subtract 3
`x = -1`

So, you see that the main point is that you don't have to follow the order of operations as such, you just have to know how to apply the properties of the algebraic operations. For example if in the first example I had divided out the 7, but didn't divide the 9 by 7, I would have gotten the wrong answer. So, you do have to know the algebraic operations very well.
• In the challenges that go with this video, they keep mentioning 'distributing'. Could someone explain how to distribute a number? Thanks very much. • Sarah,
you distribute if there is an equation such as
5(3x+4) = 50
as there is no way to add 3x and 4, we use distributive property.
Distributive property is multiplying the numbers in parentheses by the number outside
the parentheses. For a more visual example,
(5*3x)+(5*4) = 50
You multiply 5 by 3x by doing 5 times 3, and adding an x to the end of it.
15x+20 = 50
And then, you solve the rest of the problem.
15x = 30
(divide both sides by 15)
x = 2
Hope this helps!
• How would you solve an equation like this 5n - 4n + 32. That’s more of what I’m stuck on
(1 vote) • How do you solve variables on both sides in complicated equations?
(1 vote) • How did he write on the question?
(1 vote) • My 7th grade math class is pretty easy, I can get an easy A on most things and not even have to study or take notes other than the ones required. I usually can figure stuff out, like these two step problems, in my head. Yet tomorrow is math finals and they're asking us to label our steps we used to solve. I don't do any of these things that he is doing in the video, and I'm panicking! So how do we know which numbers to isolate and which numbers to divide/multiply or add/subtract? (I already know that the opposite operation is required to solve)
(1 vote) ## 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.