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## Pre-algebra

### Unit 12: Lesson 3

Number of solutions to 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?
• Yes. A square root function (later on in mathematics) basically creates a symmetrical parabola (a curve) that may cross through two points on a line. Therefore an equation can have more than one solution but not infinite solutions, but linear equations will only have one solution, no solution or infinite solutions.
• 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?
• 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?
• when you multiply negative and positive numbers what answer do you get?
• Negative times negative=positive
Positive times positive=positive
Negative times positive=negative
Positive times negative=negative

Hope it helps
(1 vote)
• 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!
• Why do we need to know how many solutions there are to each equation??
P.S. I’m not meaning to be sarcastic or rude, I’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 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?