Solve f(3-x)-f(x+2)=242

$$f ( 3 - x ) - f ( x + 2 ) = 242$$

Solve for f

$$f=\frac{242}{1-2x}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

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

$$3f-fx-f\left(x+2\right)=242$$

Use the distributive property to multiply f by x+2.

$$3f-fx-\left(fx+2f\right)=242$$

To find the opposite of fx+2f, find the opposite of each term.

$$3f-fx-fx-2f=242$$

Combine -fx and -fx to get -2fx.

$$3f-2fx-2f=242$$

Combine 3f and -2f to get f.

$$f-2fx=242$$

Combine all terms containing f.

$$\left(1-2x\right)f=242$$

Divide both sides by 1-2x.

$$\frac{\left(1-2x\right)f}{1-2x}=\frac{242}{1-2x}$$

Dividing by 1-2x undoes the multiplication by 1-2x.

$$f=\frac{242}{1-2x}$$

Solve for x

$$x=\frac{1}{2}-\frac{121}{f}$$

$$f\neq 0$$

Steps for Solving Linear Equation

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

$$3f-fx-f\left(x+2\right)=242$$

Use the distributive property to multiply f by x+2.

$$3f-fx-\left(fx+2f\right)=242$$

To find the opposite of fx+2f, find the opposite of each term.

$$3f-fx-fx-2f=242$$

Combine -fx and -fx to get -2fx.

$$3f-2fx-2f=242$$

Combine 3f and -2f to get f.

$$f-2fx=242$$

Subtract f from both sides.

$$-2fx=242-f$$

The equation is in standard form.

$$\left(-2f\right)x=242-f$$

Divide both sides by -2f.

$$\frac{\left(-2f\right)x}{-2f}=\frac{242-f}{-2f}$$

Dividing by -2f undoes the multiplication by -2f.

$$x=\frac{242-f}{-2f}$$

Divide 242-f by -2f.

$$x=\frac{1}{2}-\frac{121}{f}$$