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 (all content)

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

Lesson 9: Analyzing the number of solutions to linear equations

# Creating an equation with infinitely many solutions

Sal shows how to complete the equation 4(x - 2) + x = 5x + __ so that it has infinitely many solutions. Created by Sal Khan.

## Want to join the conversation?

• is it possible for an equation to have more than one solution but not infinite?
• It is possible for other equations (e.g., quadratic equations) to have more than one solution, but in terms of linear, no.
• Is there a faster way to find out what math problems are infinite solutions? I do the problems and then see if they are infinite, but it takes a long time...
• I simplify each side of the equation. If they are the same, then you've got infinitely many solutions.
Here is an example:
23x-5-12x=11(x-1)-6 is equal to 11x-5=11x-5
Hope this helps. God bless!
• is anyone else finding this too be incredibly difficult? like I have watched this video numerous times but the subject is still extremely difficult and foreign for my brain to wrap around. am I stupid or is it a difficult subject?
• Creating problems is a much hinger level thinking process than just solving. In this case, the idea is that you have to create something that makes both the right side of the equation and the left side to be equal to each other which gives you an infinite number of solutions. so if you have 5x-8 on the left, you need 5x-8 on the right for everything to cancel and end up with 0=0.
What do you think would be the answer to the "?" in 3x + 6 = 3(x + ?) to have infinite solutions?
• when you multiply negative and positive numbers what answer do you get?
• You get a negative number- negative*positive=negative.

For an example: -2*3=-6.
• Why do we need to know how many solutions there are to each equation??
P.S. Iโm not meaning to be sarcastic or rude, Iโm genuinely asking!
• When you are asked to solve an equation, you are being asked to find all values that will make the equation be true. Equations with one variable that are linear equation have 3 possible solution scenarios.
1) The variable has one solution
2) The equation is a contradiction (always false), so it has no solutions.
3) The equation is an identity (always true), so the variable has a solution set of all real numbers. In other words, any number you can imagine will make the equation be true. In this scenario, there are infinite solutions.

Understand the number of solutions helps you to identify what is the solution set to the equation.
• I am working multistep equations with variables on both sides and I do not understand how to work the problems and am very confused. I have problems for example like f(b)=2b+6
g(b)=b+3
Can you please show me how to work problems such as this?
• I don't get what he says at because if 4x-8+x wouldn't it be 4x minus a positive x because if we remove the 8 then it would be 4x-x and that would give us 3x. I need help. I have a math test about equations please help!
• Well this reply will be too late. But when you remove/transfer a number, you take the operation sign with it:
4x-8+x=5-8
4x+x=5xI added 8 to both sides,They cancelled out
5x=5x
• Why so many questions?
• why did sal add 4x + x? i know like x is 1 but the equation shows 4x - 8 +x like that doesn't alow it in math?
(1 vote)
• It is not clear what you think is not allowed.
The commutative property of addition, lets use reorder the terms in 4x-8+x to get 4x+x-8. Then, combine (add) 4x+1x = 5x. So the expression becomes: 5x-8

Hope this helps.