What is an inconsistent equation? Give an example.

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Hello. Today we are asked to figure out which one of our choices is an inconsistent system. And in order to figure that out, we're gonna have to go through each choice until we end up with an inconsistent system. So let's go ahead and start with a A. is two times X -4 equal to two X minus eight. Now in order to simplify this, we need to first go ahead and distribute this to to the quantity X minus four. Doing so is going to give us two x minus eight equal to two X minus eight. And to simplify this further, we can go ahead and add eight to both sides of this equation, leaving us with two X equal to two X. And if we divide both sides by two, what we are left with is X is equal to X. Now what this is is an identity equation but this is not an inconsistent equation. So we can go ahead and remove a as a possible option. Now let's go ahead and go to our option. B. B gives us the equation y plus X is equal to one. Well if we sulfur Y. By subtracting X to both sides of this equation, what we are left with is why is equal to negative X plus one. This is an equation of a line which doesn't associate itself with an inconsistent equation. So we can go ahead and remove B. As a possible option. Now let's go ahead and check option C. Option C gives us the equation five X plus five equal to five times X minus one. In order to simplify this, we need to distribute five to the quantity X minus one. Doing so gives us five X plus five equal to five x minus five. Now, in order to simplify this we can go ahead and subtract five from both sides of this equation. Doing so is going to give us five X equal to five X minus 10. And if we subtract five X from both sides of this equation, What we are left with is zero equal to negative 10. Now this is an inconsistent equation because it's saying that one quantity is equal to another which is false, so the solution or at least the inconsistent equation amongst all these options is going to be seen. So I hope this video helps you understand what an inconsistent equation is and I'll go ahead and see you all in the next video.

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