Creating an equation with infinitely many solutions
About this video
Sal builds a linear equation with infinitely many solutions. He simplifies the left side, 4(x - 2) + x, to 5x - 8, and then picks -8 as the blank in 5x + blank so both sides are identical. Subtracting 5x from both sides gives -8 = -8, true for any x.
You'll be able to
- simplify an expression using the distributive property and combining like terms.
- create an equation with infinitely many solutions by making both sides identical.
Key words
- infinitely many solutions
- Every value of x makes the equation true, because both sides are the same.
- distribute
- Multiply a number by each term inside parentheses.
- like terms
- Terms with the same variable part, like 4x and x, which can be added.
Transcript
We're asked to use the drop-down to form a linear equation with infinitely many solutions. So an equation with infinitely many solutions essentially has the same thing on both sides, no matter what x you pick. So first, my brain just wants to simplify this left-hand side a little bit and then think about how I can engineer the right-hand side so it's going to be the same as the left no matter what x I pick.
So right over here, if I distribute the 4 over x minus 2, I get 4x minus 8. And then I'm adding x to that. And that's, of course, going to be equal to 5x plus blank. And I get to pick what my blank is. And so 4x plus x is 5x. And of course, we still have our minus 8.
And that's going to be equal to 5x plus blank. So what could we make that blank so this is true for any x we pick? Well, over here we have 5 times an x minus 8. Well, if we make this a minus 8, or if we subtract 8 here, or if we make this a negative 8, this is going to be true for any x.
So if we make this a negative 8, this is going to be true for any x you pick. You give me any x, you multiply it by 5 and subtract 8, that's, of course, going to be that same x multiplied by 5 and subtracting 8. And if you were to try to somehow solve this equation, subtract 5x from both sides, you would get negative 8 is equal to negative 8, which is absolutely true for absolutely any x that you pick.
So let's go-- let me actually fill this in on the exercise. So I want to make 5-- it's going to be 5x plus negative 8.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.