In Exercises 15–35, solve each equation. Then state whether the e...

Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0

Accepted Answer

Hello. Today we're going to be solving an equation and determining whether it is identity, conditional or inconsistent. So the equation given to us is two minus three times three X plus five -5 times x -2 equal to zero. So we're gonna want to go ahead and sulfur X in this case. And in order to start that let's go ahead and open up these parentheses here in order to do that. We're gonna go ahead and distribute the values in front of them into the parentheses themselves. Doing so is gonna give me two minus three times three which is nine X negative three times five which is negative negative five times X which is negative five X. And negative five times negative two which is positive 10 and all of that is going to be equal to zero. Now what I'm going to go ahead and do is combine like terms the like terms here are negative nine X. And negative five X. Combining those together is going to give me negative X. And I can go ahead and combine positive to negative 15 and positive 10 together. Doing so is going to give me negative three and all of that is going to equal to zero. Next I'm gonna go ahead and move our constants to the right hand side of the equation. So all I'm gonna do is go ahead and add three to both sides. Doing so is going to leave me with negative 14 X equal to three. And in order to get X by itself I'm just gonna go ahead and divide both sides by negative 14. Doing so is going to give me X equal to negative 3/14. Now notice that we only have one solution here recall that when you only have one solution for an equation, that means that the equation is going to be conditional. So since this is a conditional equation, that means that our answer is going to be a. So I hope this video helps you identify what a conditional equation is, and I'll go ahead and see you all in the next video.

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