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. 2(x-4)+3(x+5)=2x-2

Accepted Answer

Hello Today we're gonna be solving an equation and determining whether that equation is conditional identity or inconsistent. So the equation given to us is three times x plus 4 -1 - equal to X -8. Now before we start solving for X, let's go ahead and open up these parentheses in order to do that. I'm gonna take positive three and distribute it to every term here and take this minus minus sign and distribute it to every term here. Doing so is going to give me three X plus minus X plus four equal to x minus eight. Now I'm gonna go ahead and combine like terms on the left hand side of the equation. The like terms here are gonna be three X. And negative X. Combining those together is going to give me two X. And I can go ahead and combine positive 12 and positive four. Doing so is going to give me 16 and that's going to be equal to X -8. Now I'm gonna go ahead and sell for X by subtracting the X to both sides. Doing so is going to give me X plus 16 equal to negative eight. And if I subtract 16 to both sides afterward, that's going to give me X equal to negative 24 and that's going to be our solution to this equation. Now, what this also means is that we only have one solution, recall that when you only have one solution that means that your equation is going to be conditional. And since we know that we have a conditional equation the solution to this problem is going to be a. So I hope this video helps you identify whether an equation is conditional or not, and I'll see you all in the next video.

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