Solve 1/5-4/2=12/5k-3/2k

$$\frac { 1 } { 5 } - \frac { 4 } { 2 } = \frac { 12 } { 5 } k - \frac { 3 } { 2 } k$$

Solve for k

$$k=-2$$

Steps for Solving Linear Equation

Divide 4 by 2 to get 2.

$$\frac{1}{5}-2=\frac{12}{5}k-\frac{3}{2}k$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{1}{5}-\frac{10}{5}=\frac{12}{5}k-\frac{3}{2}k$$

Since \frac{1}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-10}{5}=\frac{12}{5}k-\frac{3}{2}k$$

Subtract 10 from 1 to get -9.

$$-\frac{9}{5}=\frac{12}{5}k-\frac{3}{2}k$$

Combine \frac{12}{5}k and -\frac{3}{2}k to get \frac{9}{10}k.

$$-\frac{9}{5}=\frac{9}{10}k$$

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

$$\frac{9}{10}k=-\frac{9}{5}$$

Multiply both sides by \frac{10}{9}, the reciprocal of \frac{9}{10}.

$$k=-\frac{9}{5}\times \frac{10}{9}$$

Multiply -\frac{9}{5} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$k=\frac{-9\times 10}{5\times 9}$$

Do the multiplications in the fraction \frac{-9\times 10}{5\times 9}.

$$k=\frac{-90}{45}$$

Divide -90 by 45 to get -2.

$$k=-2$$