What is a conditional equation? Give an example.

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Hello Today we are asked to find which one of these options matches the conditions for a conditional equation. So in order to figure that out, we're gonna have to go through each of our options and simplify them. So let's go ahead and start with option A option A gives us the equation two times the quantity X minus four equal to two, X minus eight. Now, in order to simplify this we need to go ahead and distribute to to the quantity X minus four. Doing so is going to give us two x minus eight equal to two X minus eight. To simplify this further, we can go ahead and add eight to both sides of this equation, leaving us with two X equal to X. And if we divide both sides of this equation by two we are left with X is equal to X. Now this is saying that this variable is equal to itself. So this is the conditions for an identity equation but this is not the conditions for a conditional equation. So we can go ahead and remove option A as our solution. Now let's go ahead and check option B. Option B gives us the equation, Y plus X is equal to one. Well, if we solve for Y by subtracting X to both sides of this equation, what this gives us is Y is equal to negative X plus one. This is the equation for a line which doesn't associate itself with conditional equation so we can go ahead and remove B as a possible option. Now let's go ahead and check statement C. 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 is going to give us the equation five X plus five equal to five X minus five. To simplify this, we can subtract five from both sides of the equation that leaves us with five X equal to five X minus 10. And if we subtract five X from both sides of the equation, What we are left with is zero equal to negative 10 While zero equal to negative 10 is and inconsistent equation because it's saying that this quantity is equal to another quantity quantity which is false. So C is not going to be our solution. Now let's check option D Dean gives us the equation six X plus three equal to nine X minus three. In order to simplify this, we can go ahead and add three to both sides of the equation. Doing so is going to give us six X plus six equal to nine X. And if we subtract six x from both sides, what we are left with is six equal to three X. And finally, if we divide both sides of this equation by three, we are left with three equal to X or X is equal to three. Now what this is saying is that there is only one solution for this equation and that's when X is equal to three. This is the condition for a conditional equation, so that means that the solution is going to be D. So I hope this video helps you in understanding how to identify a conditional equation, and I'll go ahead and see you all in the next video.

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