What is a conditional equation? Give an example.

Question

Accepted Answer

Hello, today we're going to go through each of the given choices and determine which of them is a conditional equation. So let's go ahead and start with option a option A gives us the equation two times the quantity X minus four is equal to two X minus eight. Now, the first thing that we can go ahead and do is divide the entire equation by two and dividing everything by two is going to leave us with X -4 is equal to two, x divided by two, which is going to leave us with X -8 divided by two, which is going to give us four. Now, the next thing we can go ahead and do is add four to both sides of the equation and adding forward to both sides of the equation is just going to cancel up both of the fours leaving us with X is equal to X. Now, since we have X is equal to X, this means that X is going to be equal to itself, which is the condition for an identity statement. So that means the option A is not going to be a conditional equation. It's an identity equation. Let's go ahead and choose or check option B now. So option B states that we have Y plus X Is equal to one. Now, in this case here, this is the standard form of the equation of a line and this is not going to be a conditional equation. So option B is not going to be the answer. Now, let's check. Option C option C gives us the equation five, X plus five is equal to five times the quantity X minus one. The first thing that we can do to simplify this is we can divide everything by five and dividing every term in the equation by five is going to give us five X divided by five which is going to give us X plus five divided by five which is going to give us one and that is going to equal to X minus one. Now, what we can go ahead and do is subtract one to both sides of the equation and that's going to give us X is equal to X -2. And finally, we can subtract X to both sides of the equation. And that's going to cancel out both of the X is leaving us with zero is equal to negative two. Now, in this case here, zero cannot equal to negative two. So this is the condition for inconsistent statement. And that means that option C is not going to be the answer. Now, let's check option D option D gives us the equation six X plus three is equal to nine X minus three. Now looking at the coefficients of every term here, 639 and three are all divisible by three. So let's go ahead and simplify this equation by dividing, dividing everything by three. That's going to give us two X plus one is equal to three X minus one. And now in order to solve for X, we can go ahead and subtract two X to both sides of the equation. And we can add one to both sides of the equation. Doing this is going to leave us with two is equal to X. And what this means is that there is only going to be one solution for X, which is the condition for a conditional statement. And that means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

What is a conditional equation? Give an example.

Key Concepts

Conditional Equation

Solution of an Equation

Example of a Conditional Equation

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