Solve 2ax=19(10^-x+1)-19(10^x+1)

$$2 a x = 19 ( 10 ^ { - x } + 1 ) - 19 ( 10 ^ { x } + 1 )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{19\left(100^{x}-1\right)}{2x\times 10^{x}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 19 by 10^{-x}+1.

$$2ax=19\times 10^{-x}+19-19\left(10^{x}+1\right)$$

Use the distributive property to multiply -19 by 10^{x}+1.

$$2ax=19\times 10^{-x}+19-19\times 10^{x}-19$$

Subtract 19 from 19 to get 0.

$$2ax=19\times 10^{-x}-19\times 10^{x}$$

The equation is in standard form.

$$2xa=\frac{19}{10^{x}}-19\times 10^{x}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{\frac{19}{10^{x}}-19\times 10^{x}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{\frac{19}{10^{x}}-19\times 10^{x}}{2x}$$

Divide -19\times 10^{x}+\frac{19}{10^{x}} by 2x.

$$a=\frac{\frac{19}{2\times 10^{x}}-\frac{19\times 10^{x}}{2}}{x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{19\left(100^{x}-1\right)}{2x\times 10^{x}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 19 by 10^{-x}+1.

$$2ax=19\times 10^{-x}+19-19\left(10^{x}+1\right)$$

Use the distributive property to multiply -19 by 10^{x}+1.

$$2ax=19\times 10^{-x}+19-19\times 10^{x}-19$$

Subtract 19 from 19 to get 0.

$$2ax=19\times 10^{-x}-19\times 10^{x}$$

The equation is in standard form.

$$2xa=\frac{19}{10^{x}}-19\times 10^{x}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{\frac{19}{10^{x}}-19\times 10^{x}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{\frac{19}{10^{x}}-19\times 10^{x}}{2x}$$

Divide -19\times 10^{x}+\frac{19}{10^{x}} by 2x.

$$a=\frac{\frac{19}{2\times 10^{x}}-\frac{19\times 10^{x}}{2}}{x}$$