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. 2x/3 = 6 - x/4

Accepted Answer

Hello. Today we're going to be solving an equation for X. And determining whether that equation is conditional, identical or inconsistent. So the equation gave into us is five X over six equal to 3 -2 x over seven. Now, since we're solving for X, let's go ahead and set this equation equal to zero in order to do that. I'm just gonna take this quantity and move it over to the other side by subtraction. Doing so is gonna give me five X over six minus three minus two X over seven equal to zero. Now I want to go ahead and combine these fractions together in order to do that. I need to figure out what the lowest common denominator for six and 7 is. While the lowest common denominator for six and 7 is going to be 42. In order to get 42 for both fractions I need to multiply the first one by seven and the second one by six doing so is going to give me seven times five X over -6 times 3 -2 x over 42. And that is going to equal to zero. Now since both of these fractions have a similar denominator I can go ahead and combine them into a single fraction. Doing so is going to give me seven times five x minus six times three minus two X. All of that is going to be over 42 And it's going to be equal to zero. Now I can go ahead and get rid of the denominator right now by multiplying both sides by 42. Doing so is gonna leave me with seven times 5 X -6 times 3 -2 x equal to zero. Now we can go ahead and sulfur X. In order to start that let's go ahead and open up the parentheses. So we're gonna multiply seven and five X together and distribute negative six to every term in this parentheses here seven times five X is going to give me 35 X negative six times three is going to give me negative 18 and negative six times negative two X. Is going to give me positive 12 X. And all of that is going to equal to zero. Now we want to go ahead and combine like terms the like terms here are going to be 35 X. And 12 X adding those two together is going to give me 47 X. And that's going to be minus 18 equal to zero. Now let's go ahead and add 18 to both sides to try to get X by itself. Doing so is gonna leave me with 47 x equal to 18. And now in order to get X by itself, we're just gonna divide both sides by 47 And that's gonna give me x equal to 18/47. And that will be the solution to this equation. Now this means there's only one solution to this equation when there is only one solution. That means that this equation is going to be conditional. So since this equation is conditional, that means the solution to this problem is going to be a So I hope this video helps you reduce and self rational functions and also determine whether the equation is conditioned or not, and I'll go ahead and see you all in the next video.

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