Solve 3y-1/3=1/2y-4

$$3 y - \frac { 1 } { 3 } = \frac { 1 } { 2 } y - 4$$

Solve for y

$$y = -\frac{22}{15} = -1\frac{7}{15} \approx -1.466666667$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}y from both sides.

$$3y-\frac{1}{3}-\frac{1}{2}y=-4$$

Combine 3y and -\frac{1}{2}y to get \frac{5}{2}y.

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

Add \frac{1}{3} to both sides.

$$\frac{5}{2}y=-4+\frac{1}{3}$$

Convert -4 to fraction -\frac{12}{3}.

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

Since -\frac{12}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add -12 and 1 to get -11.

$$\frac{5}{2}y=-\frac{11}{3}$$

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$y=-\frac{11}{3}\times \frac{2}{5}$$

Multiply -\frac{11}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-11\times 2}{3\times 5}$$

Do the multiplications in the fraction \frac{-11\times 2}{3\times 5}.

$$y=\frac{-22}{15}$$

Fraction \frac{-22}{15} can be rewritten as -\frac{22}{15} by extracting the negative sign.

$$y=-\frac{22}{15}$$