Exercises 137–139 will help you prepare for the material covered ...

Question

Exercises 137–139 will help you prepare for the material covered in the next section.Solve for x: a(x - 2) = b(2x + 3)

Accepted Answer

Hello. Today we're going to be solving for X. In the given equation. So the equation is G. Times the quantity X minus three is equal to D. Times the quantity four X plus eight. Now I need to simplify both the left and right hand side of this equation. So what I can go ahead and do is distribute G into the quantity X minus three and distribute D into the quantity four X plus eight. Doing so is going to give me G. X minus three. G. Is equal to four D. X plus eight D. Now since we're solving for X let's go ahead and get all the X terms to one side of the equation and all the non X terms to the other side. So what we can go ahead and do is subtract four D. X to both sides of the equation and add three G to both sides. And doing so is going to give me G. X minus four D. X. Is equal to three G plus eight D. Now on the left hand side both of these terms have a common factor X. So we can go ahead and factor out an X. From both terms. And doing so is going to give me X times the quantity G minus four D. Is equal to three G plus eight D. Now one more step into solving X. I want to get X by itself. So we can go ahead and divide both sides by the quantity G minus four D. And doing so is going to give me X. Is equal to three G plus eight G. All over G minus four D. And this is going to be the solution for X. But now we need to figure out what the domain is. Now. The domain of a rational function is anywhere where X cannot equal to zero. So we're gonna take our given don't denominator which is G minus four D. And said it not equal to zero. And now we just need to solve, well I can go ahead and add four D to both sides of this equation. So G cannot equal to four D. And I want to get D by itself so I can go ahead and divide both sides by four and D. Cannot equal G over four. And that's gonna be the domain of this X value. So X is equal to three G plus eight D. Over G minus four D. And D. Cannot equal to G over four. So that's gonna be the solution to this equation. And that means the answer to this problem is going to be C. So I hope this video helps you in understanding how to solve this type of equation. And I'll go ahead and see you all in the next video

Struggling with College Algebra?

Exercises 137–139 will help you prepare for the material covered in the next section.Solve for x: a(x - 2) = b(2x + 3)

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