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### 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?
• Wrath,
No.
But, you could divide both sides by 5 first,
and then you would need to add (11/5) (instead of 11) to both sides.

5x - 11 = 42 Divide both sides by 5
x - 11/5 = 42/5 Now add (11/5) to both sides
x = 42/5 + 11/5 = 53/5
• solve the equation s+j=a for j
• All you will need to do is subtract s from both sides to isolate the variable j.
(1 vote)
• 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!