Answer:
The value of x is, ![x= \frac{17N+r}{34-N}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B17N%2Br%7D%7B34-N%7D)
Explanation:
Given: ![N(17+x)=34x-r](https://tex.z-dn.net/?f=N%2817%2Bx%29%3D34x-r)
Distributive Property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately.
If ![a\cdot(b+c) =a\cdot b + a\cdot c](https://tex.z-dn.net/?f=a%5Ccdot%28b%2Bc%29%20%3Da%5Ccdot%20b%20%2B%20a%5Ccdot%20c)
Now, using distributive property on left hand side of the given expression as:
or ![17N+Nx = 34x-r](https://tex.z-dn.net/?f=17N%2BNx%20%3D%2034x-r)
Addition Property of equality state that we add the same number from both sides of an equation.
Add r to both sides of an equation:
![17N+Nx+r=34x-r+r](https://tex.z-dn.net/?f=17N%2BNx%2Br%3D34x-r%2Br)
Simplify:
![17N+Nx+r=34x](https://tex.z-dn.net/?f=17N%2BNx%2Br%3D34x)
Subtraction Property of equality state that we subtract the same number from both sides of an equation.
Subtract Nx from both sides of an equation;
![17N+Nx+r-Nx=34x-Nx](https://tex.z-dn.net/?f=17N%2BNx%2Br-Nx%3D34x-Nx)
Simplify:
or
![17N+r=x(34-N)](https://tex.z-dn.net/?f=17N%2Br%3Dx%2834-N%29)
Division Property of equality states that we divide the same number from both sides of an equation.
Divide by (34-N) to both sides of an equation;
![\frac{17N+r}{34-N}= \frac{x(34-N)}{34-N}](https://tex.z-dn.net/?f=%5Cfrac%7B17N%2Br%7D%7B34-N%7D%3D%20%5Cfrac%7Bx%2834-N%29%7D%7B34-N%7D)
On Simplify:
![x= \frac{17N+r}{34-N}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B17N%2Br%7D%7B34-N%7D)