Solve each equation for x. 3x=(2x-1)(m+4)

Question

Accepted Answer

Hey everyone here we are asked to write the value of Y. In terms of P. For our given equation where we have nine Y is equal to the quantity of three Y minus one times the quantity of P plus two. Now to write the value of Y, we just need to solve our given equation for Y, which means we first need to focus on getting all of the Y terms on one side of the equation. So we can start by moving the nine Y from the left hand side of the equation to the right hand side. So we need to divide both sides of the equation by nine Y. And we see on the left hand side nine Y divided by nine Y cancels. So we just have one is equal to the quantity of three, Y minus one times the quantity of P plus two, all divided by nine Y. So now on the right hand side we see that we have this P plus two in the numerator. Well we are trying to get all of the Y terms alone. So we need to move this P plus two to the left hand side of our equation which means we have to divide both sides by the quantity of P plus two. And now simplifying, we see on the right hand side that the P plus twos cancel. So we are left with one divided by the quantity of P plus two is equal to the quantity of three Y minus one divided by nine Y. And now on the right hand side of our equation we can actually break up this fraction into two individual fractions. So doing this we have one divided by the quantity of P plus two is equal to three Y divided by nine y minus one divided by nine Y. And so now we can simplify our first fraction here, so we have one divided by the quantity of P plus two is equal to three Y, divided by nine Y. Which simplifies to one third minus one divided by nine Y. And so now we want to move over this one third from the right hand side to the left hand side. So that means we need to subtract one third from both sides. And now doing this here we will get one divided by P plus two minus one third is equal to negative one divided by nine Y. So now on the left hand side we want to simplify these two fractions by subtracting the first fraction from the second. So this means that we need to have common denominators. So beginning with our first fraction where we have one divided by the quantity of P plus to well to get a common denominator we need to multiply the numerator and the denominator by the value in the denominator of the second fraction. So here we multiply our first fraction, the numerator and the denominator by three. And now we have minus one third. And for this fraction we need to multiply the numerator. And the denominator by P plus two. And again this expression here is equivalent to negative one divided by nine Y. So now we just need to simplify our products and we end up with three divided by the quantity of P plus two minus the quantity of P plus two, divided by three times the quantity of P plus two. And this is equal to negative one divided by nine Y. And so now we have found our common denominators here. The first denominator should have been three times the quantity of P plus two. But so now we have common denominators and we can go ahead and combine the enumerators. So combining the numerator as we have three minus the quantity of P plus two. All divided by three times the quantity of P plus two. This is equal to negative one divided by nine Y. And now we just need to simplify our numerator here. So going up to the top of the page here we have three minus the quantity of P plus two which simplifies to negative P plus or sorry negative yeah negative P plus one. All divided by three times the quantity of P plus two. And again this is equal to negative one divided by nine Y. And so now our next step we can get rid of this negative sign on the right hand side by multiplying both sides by -1. So again we multiply both sides by negative one. So distributing this negative one on the on the left hand side of our equation. We get p minus one all divided by three times the quantity of P plus two. And again this is equal to now the right hand side becomes one divided by nine Y. And now we see that on the right hand side we we have Y in the denominator but we want it in the numerator. So that means we need to take the inverse of both sides, so doing the inverse of both sides. Our left hand side becomes three times the quantity of P plus two, all divided by p minus one. And now the right hand side just becomes nine Y. And so now to finish getting why alone on the right hand side we just have to get rid of the coefficient. So we just need to divide both sides by nine. And so we see that y alone is equal to the quantity of three times the quantity of P plus two divided by the quantity of P minus one divided by nine, which is also equal two times one. Ninth. So now just simplifying, we see that the three in the numerator becomes one and the nine and the denominator becomes three. So we see that Y is equivalent to the quantity of P plus two divided by three times the quantity of p minus one. So now we have fully isolated our Y value. So we have solved for the value of Y in terms of the variable P. So this is our final answer here, which is answer choice. A thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Solve each equation for x. 3x=(2x-1)(m+4)

Key Concepts

Linear Equations

Distributive Property

Isolating the Variable

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