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### Course: Integrated math 1>Unit 2

Lesson 3: 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?
• 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.
• 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.
• 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!
• It is 4x-8+x. This can be rearranged to 4x+x-8. You subtract the 8 no matter how you rearrange the expression, not the x. You add the x. The signs of variables and/or numbers in an expression never change, no matter how you rearrange them.
• I really am struggling with creating/identifying the solutions, infinite solutions, and no solutions.
• To find the number of solutions of a linear equation, it is not necessary to go through all the equation solving steps! It is enough just to simplify each side, that is, to remove parentheses (using the distributive property) and combine like terms on each side separately.

Then compare coefficients and constants on both sides:

1) if the coefficients on the variable are different on both sides, then there’s exactly one solution regardless of how the constant terms compare, and

2) if the coefficients on the variable are the same on both sides:

a) there are infinitely many solutions if the constant terms are also the same on both sides, and

b) there are no solutions if the constant terms are different on both sides.

Have a good day!
• Why so many questions?
• what does Sal mean when he says "any X"?
• The solution to the equation is: x = all real numbers. You randomly pick any number to use for x, plug it into the equation, and the 2 sides of the equation will be equal. So, it will be a solution to the equation.

Hope this helps.