Solve 1.3x=Ax+Bx+x

$$1.3 x = A x + B x + x$$

Solve for A (complex solution)

$$\left\{\begin{matrix}\\A=0.3-B\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Ax+Bx+x=1.3x$$

Subtract Bx from both sides.

$$Ax+x=1.3x-Bx$$

Subtract x from both sides.

$$Ax=1.3x-Bx-x$$

Combine 1.3x and -x to get 0.3x.

$$Ax=0.3x-Bx$$

The equation is in standard form.

$$xA=-Bx+\frac{3x}{10}$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{x\left(0.3-B\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{x\left(0.3-B\right)}{x}$$

Divide x\left(0.3-B\right) by x.

$$A=0.3-B$$

Solve for B (complex solution)

$$\left\{\begin{matrix}\\B=0.3-A\text{, }&\text{unconditionally}\\B\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Ax+Bx+x=1.3x$$

Subtract Ax from both sides.

$$Bx+x=1.3x-Ax$$

Subtract x from both sides.

$$Bx=1.3x-Ax-x$$

Combine 1.3x and -x to get 0.3x.

$$Bx=0.3x-Ax$$

The equation is in standard form.

$$xB=-Ax+\frac{3x}{10}$$

Divide both sides by x.

$$\frac{xB}{x}=\frac{x\left(0.3-A\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$B=\frac{x\left(0.3-A\right)}{x}$$

Divide x\left(0.3-A\right) by x.

$$B=0.3-A$$

Solve for A

$$\left\{\begin{matrix}\\A=0.3-B\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Ax+Bx+x=1.3x$$

Subtract Bx from both sides.

$$Ax+x=1.3x-Bx$$

Subtract x from both sides.

$$Ax=1.3x-Bx-x$$

Combine 1.3x and -x to get 0.3x.

$$Ax=0.3x-Bx$$

The equation is in standard form.

$$xA=-Bx+\frac{3x}{10}$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{x\left(0.3-B\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{x\left(0.3-B\right)}{x}$$

Divide x\left(0.3-B\right) by x.

$$A=0.3-B$$

Solve for B

$$\left\{\begin{matrix}\\B=0.3-A\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Ax+Bx+x=1.3x$$

Subtract Ax from both sides.

$$Bx+x=1.3x-Ax$$

Subtract x from both sides.

$$Bx=1.3x-Ax-x$$

Combine 1.3x and -x to get 0.3x.

$$Bx=0.3x-Ax$$

The equation is in standard form.

$$xB=-Ax+\frac{3x}{10}$$

Divide both sides by x.

$$\frac{xB}{x}=\frac{x\left(0.3-A\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$B=\frac{x\left(0.3-A\right)}{x}$$

Divide x\left(0.3-A\right) by x.

$$B=0.3-A$$