Solve (1-2omega_{0})x=x

$$( 1 - 2 \omega _ { 0 } ) x = x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&\omega _{0}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-2\omega _{0} by x.

$$x-2\omega _{0}x=x$$

Subtract x from both sides.

$$x-2\omega _{0}x-x=0$$

Combine x and -x to get 0.

$$-2\omega _{0}x=0$$

The equation is in standard form.

$$\left(-2\omega _{0}\right)x=0$$

Divide 0 by -2\omega _{0}.

$$x=0$$

Solve for ω_0 (complex solution)

$$\left\{\begin{matrix}\\\omega _{0}=0\text{, }&\text{unconditionally}\\\omega _{0}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-2\omega _{0} by x.

$$x-2\omega _{0}x=x$$

Subtract x from both sides.

$$-2\omega _{0}x=x-x$$

Combine x and -x to get 0.

$$-2\omega _{0}x=0$$

The equation is in standard form.

$$\left(-2x\right)\omega _{0}=0$$

Divide 0 by -2x.

$$\omega _{0}=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\omega _{0}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-2\omega _{0} by x.

$$x-2\omega _{0}x=x$$

Subtract x from both sides.

$$x-2\omega _{0}x-x=0$$

Combine x and -x to get 0.

$$-2\omega _{0}x=0$$

The equation is in standard form.

$$\left(-2\omega _{0}\right)x=0$$

Divide 0 by -2\omega _{0}.

$$x=0$$

Solve for ω_0

$$\left\{\begin{matrix}\\\omega _{0}=0\text{, }&\text{unconditionally}\\\omega _{0}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-2\omega _{0} by x.

$$x-2\omega _{0}x=x$$

Subtract x from both sides.

$$-2\omega _{0}x=x-x$$

Combine x and -x to get 0.

$$-2\omega _{0}x=0$$

The equation is in standard form.

$$\left(-2x\right)\omega _{0}=0$$

Divide 0 by -2x.

$$\omega _{0}=0$$