Solve -f(x)=3/5x+2/3

$$- f ( x ) = \frac { 3 } { 5 } x + \frac { 2 } { 3 }$$

Solve for f

$$f=-\frac{3}{5}-\frac{2}{3x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Reorder the terms.

$$-fx=\frac{3}{5}x+\frac{2}{3}$$

The equation is in standard form.

$$\left(-x\right)f=\frac{3x}{5}+\frac{2}{3}$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{\frac{3x}{5}+\frac{2}{3}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{\frac{3x}{5}+\frac{2}{3}}{-x}$$

Divide \frac{3x}{5}+\frac{2}{3} by -x.

$$f=-\frac{3}{5}-\frac{2}{3x}$$

Solve for x

$$x=-\frac{10}{3\left(5f+3\right)}$$

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

Steps for Solving Linear Equation

Subtract \frac{3}{5}x from both sides.

$$\left(-f\right)x-\frac{3}{5}x=\frac{2}{3}$$

Reorder the terms.

$$-fx-\frac{3}{5}x=\frac{2}{3}$$

Combine all terms containing x.

$$\left(-f-\frac{3}{5}\right)x=\frac{2}{3}$$

Divide both sides by -f-\frac{3}{5}.

$$\frac{\left(-f-\frac{3}{5}\right)x}{-f-\frac{3}{5}}=\frac{\frac{2}{3}}{-f-\frac{3}{5}}$$

Dividing by -f-\frac{3}{5} undoes the multiplication by -f-\frac{3}{5}.

$$x=\frac{\frac{2}{3}}{-f-\frac{3}{5}}$$

Divide \frac{2}{3} by -f-\frac{3}{5}.

$$x=-\frac{10}{3\left(5f+3\right)}$$