Solve ax-1=x-a^24

$$a x - 1 = x - a ^ { 24 }$$

Solve for x

$$\left\{\begin{matrix}x=-\left(a+1\right)\left(a^{2}+1\right)\left(a^{4}+1\right)\left(a^{16}+a^{8}+1\right)\text{, }&a\neq 1\\x\in \mathrm{R}\text{, }&a=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$ax-1-x=-a^{24}$$

Add 1 to both sides.

$$ax-x=-a^{24}+1$$

Combine all terms containing x.

$$\left(a-1\right)x=-a^{24}+1$$

The equation is in standard form.

$$\left(a-1\right)x=1-a^{24}$$

Divide both sides by a-1.

$$\frac{\left(a-1\right)x}{a-1}=\frac{1-a^{24}}{a-1}$$

Dividing by a-1 undoes the multiplication by a-1.

$$x=\frac{1-a^{24}}{a-1}$$

Divide -a^{24}+1 by a-1.

$$x=-\left(a+1\right)\left(a^{2}+1\right)\left(a^{4}+1\right)\left(a^{16}+a^{8}+1\right)$$