In Exercises 71–78, solve each equation. Then determine whether t...

Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation.

4x + 7 = 7(x + 1) - 3x

Accepted Answer

Hello Today we're going to be solving an equation and determining whether that equation is conditional, identical or inconsistent. So the equation given to us is three x minus 11 equal to five times x minus one minus two times X plus three. Now, in order to start solving for X, let's go ahead and open up the parentheses in order to do that, I need to take five and distributed to every term here and take negative two and distribute to every term here. Doing so is going to leave me with three X - equal to 5, -5 -2 X -6. And I'm gonna go ahead and combine like terms on the right hand side of this equation. I can combine five x and -2 x. And that's going to give me three X. Now I can combine negative five and negative six together and that's going to give me negative 11. Now what I can do here is go ahead and add 11 to both sides and that's going to give me three X equal to three X. And in order to solve for X, I can divide both sides by three and that'll leave me with X equal to X. So what this statement means is that this variable is always going to be equal to itself whenever you have a variable equal to itself. That means that this is going to be an identity equation. It's also an indication that you have an infinite amount of solutions. So since we know that this is an identity equation, the solution to this problem is going to be be so. I hope this video helps you understand what an identity equation is, and I'll go ahead and see all in the next video.

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