I got 2 possible answers: 1. n=(A-z)/z

2. n=A/z-1

Please solve and give details for each and every step.

I got 2 possible answers: 1. n=(A-z)/z

2. n=A/z-1

Please solve and give details for each and every step.

Tutors, sign in to answer this question.

Anna,

This question is best solved by factoring. Factor the n from the right hand size of the equation, then just use algebraic rules to solve from there.

Best of luck, Steve

Philip N. | Certified 5-12 Math TeacherCertified 5-12 Math Teacher

We can use the distributive property to factor the right side of the equation for
*n*, and we get

A = nz+n **= n(z+1)**

Then, we can use the division property of equality to prepare to move *z+1* to the left side of the equation and to isolate
*n*.

A**/(z+1)** = n×(z+1)**/(z+1)**

Now, we apply the identity property of division.

A/(z+1) = n×**(z+1)/(z+1)** = n**×1 = n**

So n = A/(z+1).

We can test the solutions that you found by solving them again for A. In the first, we have the following.

n = (A-z)/z

nz = A-z

nz+z = A

Since that isn't what we started with, your solution (1) isn't correct.

For the second, we have

n = A/z-1

If that is n = (A/z)-1, then

n+1 = A/z

zn+z = A

If it is n = A/(z-1), then

n(z-1) = A

nz-n = A

That is close, but without seeing your work, it is hard to know how z+1 became z-1, which I think is where you had your error.

HTH.

Factor out n,

A = n(z+1)

Isolate n by dividing both sides by z+1,

n = A/(z+1) <==Answer

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## Comments

Apologies to Robert; my computer displayed his answer as though it had no content.