Solve 1/3+2/f=x

$$\frac { 1 } { 3 } + \frac { 2 } { f } = x$$

Solve for f

$$f=-\frac{6}{1-3x}$$

$$x\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3f, the least common multiple of 3,f.

$$3f\times \frac{1}{3}+3\times 2=x\times 3f$$

Multiply 3 and \frac{1}{3} to get 1.

$$f+3\times 2=x\times 3f$$

Multiply 3 and 2 to get 6.

$$f+6=x\times 3f$$

Subtract x\times 3f from both sides.

$$f+6-x\times 3f=0$$

Multiply -1 and 3 to get -3.

$$f+6-3xf=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$f-3xf=-6$$

Combine all terms containing f.

$$\left(1-3x\right)f=-6$$

Divide both sides by -3x+1.

$$\frac{\left(1-3x\right)f}{1-3x}=-\frac{6}{1-3x}$$

Dividing by -3x+1 undoes the multiplication by -3x+1.

$$f=-\frac{6}{1-3x}$$

Variable f cannot be equal to 0.

$$f=-\frac{6}{1-3x}\text{, }f\neq 0$$

Solve for x

$$x=\frac{1}{3}+\frac{2}{f}$$

$$f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3f, the least common multiple of 3,f.

$$3f\times \frac{1}{3}+3\times 2=x\times 3f$$

Multiply 3 and \frac{1}{3} to get 1.

$$f+3\times 2=x\times 3f$$

Multiply 3 and 2 to get 6.

$$f+6=x\times 3f$$

Swap sides so that all variable terms are on the left hand side.

$$x\times 3f=f+6$$

The equation is in standard form.

$$3fx=f+6$$

Divide both sides by 3f.

$$\frac{3fx}{3f}=\frac{f+6}{3f}$$

Dividing by 3f undoes the multiplication by 3f.

$$x=\frac{f+6}{3f}$$

Divide 6+f by 3f.

$$x=\frac{1}{3}+\frac{2}{f}$$