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

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

Solve for f

$$f=\frac{5x}{3\left(4-x\right)}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4f by 3-x.

$$fx+12f-4fx=5x$$

Combine fx and -4fx to get -3fx.

$$-3fx+12f=5x$$

Combine all terms containing f.

$$\left(-3x+12\right)f=5x$$

The equation is in standard form.

$$\left(12-3x\right)f=5x$$

Divide both sides by -3x+12.

$$\frac{\left(12-3x\right)f}{12-3x}=\frac{5x}{12-3x}$$

Dividing by -3x+12 undoes the multiplication by -3x+12.

$$f=\frac{5x}{12-3x}$$

Divide 5x by -3x+12.

$$f=\frac{5x}{3\left(4-x\right)}$$

Solve for x

$$x=\frac{12f}{3f+5}$$

$$f\neq -\frac{5}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4f by 3-x.

$$fx+12f-4xf=5x$$

Combine fx and -4xf to get -3fx.

$$-3fx+12f=5x$$

Subtract 5x from both sides.

$$-3fx+12f-5x=0$$

Subtract 12f from both sides. Anything subtracted from zero gives its negation.

$$-3fx-5x=-12f$$

Combine all terms containing x.

$$\left(-3f-5\right)x=-12f$$

Divide both sides by -3f-5.

$$\frac{\left(-3f-5\right)x}{-3f-5}=-\frac{12f}{-3f-5}$$

Dividing by -3f-5 undoes the multiplication by -3f-5.

$$x=-\frac{12f}{-3f-5}$$

Divide -12f by -3f-5.

$$x=\frac{12f}{3f+5}$$