Solve each equation for x. x/a-1 = ax+3

Question

Accepted Answer

Hey everyone here we are asked to write the value of Z. In terms of N. For the given equation where we have three, Z divided by n minus four is equal to six and Z plus five. Now to write the value of Z, we just need to manipulate our given equation so that we get the Z variable alone. So we can start by looking at the left hand side of the equation and we see that we we have three Z divided by N. Well again we want to get our Z value alone so we need to move this other term, this minus four to the right hand side. So to do this we just add four to both sides of the equation and then our equation becomes three. Z divided by N is equal to six. N. Z plus five plus four. And now just simplifying our equation is three. Z divided by N is equal to six and Z plus nine. Now to continue to get the alone on the left hand side here we want to get rid of the coefficient which is three. So to get rid of the coefficient, we just need to divide both sides of the equation by three. So with this our equation becomes the divided by N is equal to two, N. Z plus three. And now our last step to get Z alone on the left hand side of our equation is to just get rid of this denominator of N. So that means we need to just multiply both sides of our equation by the denominator which is N. So both sides get multiplied by N. And our equation becomes Z is equal to two, N squared times Z plus three N. And now taking a look at our equation so far, we see that on the right hand side of the equation, we still have a term here with the variable Z. We have two and squared times Z. And well we need Z all on one side of the equation. So we need to move this term to the left hand side of our equation by subtracting two and squared times Z from both sides. And now doing this, our equation becomes on the left hand side we have Z minus two and squared times E. Is equal to three N. So now looking at the left hand side of our equation again, we need to get the Z variable alone. Well, both terms here have the variable Z. So we can just factor out. Easy to get to get it alone. So we have Z times the quantity of one minus two and squared and this is equal to three N. And now all we need to do to get the alone is to divide both sides of the equation by this expression here, this quantity of one minus two and squared. So both sides get divided by the quantity of one minus two and squared. And with this our final equation be becomes Z is equal to three N, divided by the quantity of one minus two and squared. And with this we have fully isolated the Z variable. So we have found the value of Z in terms of the variable N. And so we are left with answer choice. C. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Solve each equation for x. x/a-1 = ax+3

Key Concepts

Algebraic Manipulation

Isolating the Variable

Understanding Fractions

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