Solve f7x+2a=3x+5a,w

$$f 7 x + 2 a = 3 x + 5 a , w$$

Solve for f_7 (complex solution)

$$\left\{\begin{matrix}f_{7}=\frac{3\left(x+a\right)}{x}\text{, }&x\neq 0\\f_{7}\in \mathrm{C}\text{, }&x=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2a from both sides.

$$f_{7}x=3x+5a-2a$$

Combine 5a and -2a to get 3a.

$$f_{7}x=3x+3a$$

The equation is in standard form.

$$xf_{7}=3x+3a$$

Divide both sides by x.

$$\frac{xf_{7}}{x}=\frac{3x+3a}{x}$$

Dividing by x undoes the multiplication by x.

$$f_{7}=\frac{3x+3a}{x}$$

Divide 3x+3a by x.

$$f_{7}=\frac{3\left(x+a\right)}{x}$$

Solve for a

$$a=\frac{x\left(f_{7}-3\right)}{3}$$

Steps for Solving Linear Equation

Subtract 5a from both sides.

$$f_{7}x+2a-5a=3x$$

Combine 2a and -5a to get -3a.

$$f_{7}x-3a=3x$$

Subtract f_{7}x from both sides.

$$-3a=3x-f_{7}x$$

Divide both sides by -3.

$$\frac{-3a}{-3}=\frac{x\left(3-f_{7}\right)}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$a=\frac{x\left(3-f_{7}\right)}{-3}$$

Divide x\left(3-f_{7}\right) by -3.

$$a=\frac{f_{7}x}{3}-x$$

Solve for f_7

$$\left\{\begin{matrix}f_{7}=\frac{3\left(x+a\right)}{x}\text{, }&x\neq 0\\f_{7}\in \mathrm{R}\text{, }&x=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2a from both sides.

$$f_{7}x=3x+5a-2a$$

Combine 5a and -2a to get 3a.

$$f_{7}x=3x+3a$$

The equation is in standard form.

$$xf_{7}=3x+3a$$

Divide both sides by x.

$$\frac{xf_{7}}{x}=\frac{3x+3a}{x}$$

Dividing by x undoes the multiplication by x.

$$f_{7}=\frac{3x+3a}{x}$$

Divide 3x+3a by x.

$$f_{7}=\frac{3\left(x+a\right)}{x}$$