Solve y=n(1^n-1x)+1-n(1^n-1)

$$y = n ( 1 ^ { n - 1 } x ) + 1 - n ( 1 ^ { n - 1 } )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y+n-1}{n}\text{, }&n\neq 0\\x\in \mathrm{C}\text{, }&y=1\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$n\times 1^{n-1}x+1-n\times 1^{n-1}=y$$

Add n\times 1^{n-1} to both sides.

$$n\times 1^{n-1}x+1=y+n\times 1^{n-1}$$

Subtract 1 from both sides.

$$n\times 1^{n-1}x=y+n\times 1^{n-1}-1$$

The equation is in standard form.

$$nx=y+n-1$$

Divide both sides by n.

$$\frac{nx}{n}=\frac{y+n-1}{n}$$

Dividing by n undoes the multiplication by n.

$$x=\frac{y+n-1}{n}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y+n-1}{n}\text{, }&n\neq 0\\x\in \mathrm{R}\text{, }&y=1\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$n\times 1^{n-1}x+1-n\times 1^{n-1}=y$$

Add n\times 1^{n-1} to both sides.

$$n\times 1^{n-1}x+1=y+n\times 1^{n-1}$$

Subtract 1 from both sides.

$$n\times 1^{n-1}x=y+n\times 1^{n-1}-1$$

The equation is in standard form.

$$nx=y+n-1$$

Divide both sides by n.

$$\frac{nx}{n}=\frac{y+n-1}{n}$$

Dividing by n undoes the multiplication by n.

$$x=\frac{y+n-1}{n}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{1-y}{x-1}\text{, }&x\neq 1\\n\in \mathrm{C}\text{, }&y=1\text{ and }x=1\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{1-y}{x-1}\text{, }&x\neq 1\\n\in \mathrm{R}\text{, }&y=1\text{ and }x=1\end{matrix}\right.$$