Solve f(-1/3)=3(-1/3-1/2(-frac{1{3})+1}

$$f ( - \frac { 1 } { 3 } ) = \frac { 3 ( - \frac { 1 } { 3 } - 1 } { 2 ( - \frac { 1 } { 3 } ) + 1 }$$

Solve for f

$$f=36$$

Steps for Solving Linear Equation

Convert 1 to fraction \frac{3}{3}.

$$f\left(-\frac{1}{3}\right)=\frac{3\left(-\frac{1}{3}-\frac{3}{3}\right)}{2\left(-\frac{1}{3}\right)+1}$$

Since -\frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$f\left(-\frac{1}{3}\right)=\frac{3\times \frac{-1-3}{3}}{2\left(-\frac{1}{3}\right)+1}$$

Subtract 3 from -1 to get -4.

$$f\left(-\frac{1}{3}\right)=\frac{3\left(-\frac{4}{3}\right)}{2\left(-\frac{1}{3}\right)+1}$$

Cancel out 3 and 3.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{2\left(-\frac{1}{3}\right)+1}$$

Express 2\left(-\frac{1}{3}\right) as a single fraction.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{\frac{2\left(-1\right)}{3}+1}$$

Multiply 2 and -1 to get -2.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{\frac{-2}{3}+1}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{-\frac{2}{3}+1}$$

Convert 1 to fraction \frac{3}{3}.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{-\frac{2}{3}+\frac{3}{3}}$$

Since -\frac{2}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{\frac{-2+3}{3}}$$

Add -2 and 3 to get 1.

$$f\left(-\frac{1}{3}\right)=\frac{-4}{\frac{1}{3}}$$

Divide -4 by \frac{1}{3} by multiplying -4 by the reciprocal of \frac{1}{3}.

$$f\left(-\frac{1}{3}\right)=-4\times 3$$

Multiply -4 and 3 to get -12.

$$f\left(-\frac{1}{3}\right)=-12$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

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

Multiply -12 and -3 to get 36.

$$f=36$$