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### 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
• Really, this video has no reason to be long. He literally solved the question at , why does the video have to continue after that.
• he needs to explain it more for people that wouldn't understand if it were put into a different equation.
• 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!
• In am equation which one is the solution and how can you tell if two equations are equivalent .
• 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?
(1 vote)
• 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!
• 0 = 0 looks like a face.
• why is this video so long
(1 vote)
• To "deepen" our understanding on equivalence
• whats the difference between linear an normal equations?
(1 vote)
• The difference between linear and nonlinear equations is as follows:

Linear Equations1:

Linear equations form a straight line or represent the equation for a straight line1.
They have only one degree1. We can also define it as an equation having the maximum degree 11.
All these equations form a straight line in the XY plane1.
The general representation of linear equation is; y = mx + c, where x and y are the variables, m is the slope of the line, and c is a constant value1.
Examples: 10x = 1, 9y + x + 2 = 0, 4y = 3x, 99x + 12 = 23y1.
Non-Linear Equations1:

Non-linear equations do not form a straight line but form a curve1.
A nonlinear equation has the degree as 2 or more than 2, but not less than 21.
It forms a curve and if we increase the value of the degree, the curvature of the graph increases1.
The general representation of nonlinear equations is; ax2 + by2 = c, where x and y are the variables and a,b and c are the constant values1.
Examples: x2 + y2 = 1, x2 + 12xy + y2 = 0, x2 + x + 2 = 251.