If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Algebra 1

### Course: Algebra 1>Unit 2

Lesson 2: Linear equations with parentheses

# Reasoning with linear equations

When we perform operations to manipulate equations, some operations produce equivalent equations, while others don't necessarily produce equivalent equations. When we're solving an equation, we need to use operations that guarantee equivalence. Created by Sal Khan.

## Want to join the conversation?

• What makes a number a non zero constant?
• Basically what he is saying is that you can divide it by any number that isnt zero. From 1 to 999999999 (and beyond), you can divide it, as long as it isn't zero. Hopefully that helped.
• hey whats up everyone just saying have a good day
• goodday!

I find it funny that i accidentally repost something and I get a message from *A_Guardian but this doesn't for months lol :D
(1 vote)
• In am equation which one is the solution and how can you tell if two equations are equivalent .
• sorry if he explained it in the video, but what does equivalence preserving mean?
(1 vote)
• Equivalence preserving means to keep the equation the same as it was before you did an operation. For example, in the video, Sal referred to the equation 2x+3=9. By subtracting 3 from both sides, he got the equation 2x=6, which is actually the same thing as 2x+3=9 and so that is what equivalence preserving means. Hope that helps!
• i do not understand this video at all
• Happy Friday everyone 😊
• Does anyone else find this video a bit confusing?? Like I get it but it could be explained better.
• What if I have 2 equations like...

A: 5x = 3x
B: 5 = 3

Since I need to divide both sides by x, wouldn't they be equivalent? How is this a non-preserving operation?
• Interesting question!

The problematic issue is the possibility of dividing both sides by zero. When you divide both sides by an expression or variable that could be zero, you can lose solutions! Note that 5x = 3x has the solution x = 0, while 5 = 3 has no solutions.

Have a blessed, wonderful day!