Solve each equation for x. 2(x-a) +b =3x+a

Question

Accepted Answer

Hey everyone here we are asked to write the value of X. In terms of M. And N. From our given equation where we have eight times the quantity of X plus n minus two M. Is equal to seven X plus M. So to find the value of X, we need to get all of our X terms on one side of the equation. And that means we first need to to factor in this eight on the left hand side of our equation. So doing this, our equation becomes eight X plus eight N minus two M. Is equal to seven X plus M. So from here we just need to manipulate this equation so we get all of the X terms on one side of the equation. So we can start with the left hand side of the equation. And we see we have eight X. Well to get eight X alone, we first need to move over the other two terms to the right hand side of the equation. So we can begin with this plus eight N. Well since eight N is positive, we need to subtract eight N from both sides so that the eight ends on the left hand side both cancel. And we are left with eight x minus two M. Is equal to seven X plus m minus eight M. And so now continuing with the left hand side of the equation, we need to now move over this minus two M. And since this term is negative we need to add to em to both sides so that the two M. S on the left hand side both canceled. And we are left with eight X is equal to seven X plus M minus eight N plus two M. So now we just need to simplify the like terms on the right hand side. So our equation becomes eight X is equal to seven X plus three M minus eight N. And now looking at our equation so far, we see that on the right hand side, we still have an X. Term this seven X. What? We want all of the X variables to be on the same side of the equation on one side of the equation. So we want to move this seven X to the left hand side of the equation so that it is with the eight X. And that means we just need to subtract seven X from both sides so that the seven X's cancel on the right hand side of the equation and we are left with eight X minus seven X is equal to three M minus eight N. And now on the left hand side we just have to simplify our X terms since they both have the same base here, the same variable of X. We can just subtract their coefficients and we see that eight X minus seven X. Just gives us X. And it is equal to three M minus eight N. And so now we see that we have completely isolated our X variable. So we have found the value of X in terms of the variables M. And N. So we are left with our final answer here, which is answer choice D. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Solve each equation for x. 2(x-a) +b =3x+a

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations

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