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

Lesson 5: Two-steps equations intro

# Two-step equations intuition

This example demonstrates how we solve an equation expressed such: ax + b = c. It's a little more complicated than previous examples, but you can do it! Created by Sal Khan.

## Want to join the conversation?

• Can zero have a negative sign before it? just wondering
• Yes. -0 = 0. Zero is neither positive nor negative, but you can put a negative sign in front of it, and that will not change the value.
• How Difficult is this kind of math problem?
• So If You get a question as easy as this here is how you do it (even is it looks hard it is still easy to do if you break it down:

you start by adding all the non-variable numbers and subtract that from the total

then you divide what's left by the number of x's or y's or whatever letter the variable is and then you add it all together. (if that is too hard i will show you in an easier way)

5x + 10 = 50
50-10= 40
40/5 = 8
8+8+8+8+8 + 10 = 50
or in other words x = 8
• Why do I need to know this-
• you dont
• can someone plz help me figure out what this means? i have a math test coming up for end of year and i need to pass ...
• It shows 3x + 5 = 17
since you are adding you will subtract 5 from 17(if you were subtracting you would add 5 to 17). Now you have 12. You have to divide 12 by 3 which equals 4 so x = 4 that is the answer.
7x - 2 = -10 you now add 2 to - 10.
Now you need to divide -8 by 7 which you can just do -8/7 or do mixed number 1 1/7. Hope this helps.
• Can someone help me with negative fractions. They are hard to understand.
• this is to hard for my sixth grade brain
• This is a hard topic to understand in my opinion...
• Is there a reason why your cancelling out the 5 instead of the 3x ?? In my engineering degree i do your method and im wrong 100% of the time, then when it shows the way to do it its always the letters that get cancelled first which results in a totally different answer......
• The properties of equality are very flexible. There is no single approach. If you apply the properties correctly (and you make no math errors), then you will get the right result.

Doing the 3x first is not usually done because you will end up working with fractions (which many people hate to work with) and fractions can require extra work steps (like finding a common denominator to add/subtract).

If you did the 3x first, here's what it would look like:
-- divide entire equation by 3: 3x/3 + 5/3 = 17/3
-- Simplify: x + 5/3 = 17/3
-- Subtract 5/3: x = 17/3 - 5/3
-- Simplify: x = 12/3 = 4
Notice, the answer is still: x=4

If by "cancelling out 3x" first, you mean subtracting 3x, then you are introducing an extra step that is not needed to solve the equation. Your goal is to isolate "x". So, you move items away from the "x", which takes 2 steps as Sal shows in the video. If you subtract 3x from both sides, then you would use 3 steps instead of 2.

Hope this helps.
FYI - You might find it more useful to post an example where you got the wrong result (along with your work steps )so someone can help you find what your are doing incorrectly.
• What was stumping me for this is trying to figure out in what order to isolate for x

you have to use reverse BEDMAS or PEMDAS, so start with addition and subtraction, and then do multiplication and division.
• The properties of equality are very flexible, they can be applied in any order. Though, some ways will lead to fewer steps and you can void working with fractions.

Keep in mind that the goal for solving equations is to geto to: x = a number.

With 2-step equations, you perform 2 steps. The most common approach is to add/subtract first to move any constant term away from the variable. Then divide by the coefficient of the variable. That doesn't mean that you can't divide first, but then you likely will need to complete the addition/subtraction using fractions.

Hope this helps.