Solve 3f(x)=4x+5f(-x)

$$3 f ( x ) = 4 x + 5 f ( - x )$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5f\left(-x\right) from both sides.

$$3fx-5f\left(-x\right)=4x$$

Multiply -1 and 5 to get -5.

$$3fx-5f\left(-1\right)x=4x$$

Multiply -5 and -1 to get 5.

$$3fx+5fx=4x$$

Combine 3fx and 5fx to get 8fx.

$$8fx=4x$$

The equation is in standard form.

$$8xf=4x$$

Divide both sides by 8x.

$$\frac{8xf}{8x}=\frac{4x}{8x}$$

Dividing by 8x undoes the multiplication by 8x.

$$f=\frac{4x}{8x}$$

Divide 4x by 8x.

$$f=\frac{1}{2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&f=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$3fx-4x=5f\left(-x\right)$$

Subtract 5f\left(-x\right) from both sides.

$$3fx-4x-5f\left(-x\right)=0$$

Multiply -1 and 5 to get -5.

$$3fx-4x-5f\left(-1\right)x=0$$

Multiply -5 and -1 to get 5.

$$3fx-4x+5fx=0$$

Combine 3fx and 5fx to get 8fx.

$$8fx-4x=0$$

Combine all terms containing x.

$$\left(8f-4\right)x=0$$

Divide 0 by 8f-4.

$$x=0$$

Solve for f

$$\left\{\begin{matrix}\\f=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5f\left(-x\right) from both sides.

$$3fx-5f\left(-x\right)=4x$$

Multiply -1 and 5 to get -5.

$$3fx-5f\left(-1\right)x=4x$$

Multiply -5 and -1 to get 5.

$$3fx+5fx=4x$$

Combine 3fx and 5fx to get 8fx.

$$8fx=4x$$

The equation is in standard form.

$$8xf=4x$$

Divide both sides by 8x.

$$\frac{8xf}{8x}=\frac{4x}{8x}$$

Dividing by 8x undoes the multiplication by 8x.

$$f=\frac{4x}{8x}$$

Divide 4x by 8x.

$$f=\frac{1}{2}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&f=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$3fx-4x=5f\left(-x\right)$$

Subtract 5f\left(-x\right) from both sides.

$$3fx-4x-5f\left(-x\right)=0$$

Multiply -1 and 5 to get -5.

$$3fx-4x-5f\left(-1\right)x=0$$

Multiply -5 and -1 to get 5.

$$3fx-4x+5fx=0$$

Combine 3fx and 5fx to get 8fx.

$$8fx-4x=0$$

Combine all terms containing x.

$$\left(8f-4\right)x=0$$

Divide 0 by 8f-4.

$$x=0$$