Solve -6y-5/3=3/4y-5/4

$$- 6 y - \frac { 5 } { 3 } = \frac { 3 } { 4 } y - \frac { 5 } { 4 }$$

Solve for y

$$y=-\frac{5}{81}\approx -0.061728395$$

Steps for Solving Linear Equation

Subtract \frac{3}{4}y from both sides.

$$-6y-\frac{5}{3}-\frac{3}{4}y=-\frac{5}{4}$$

Combine -6y and -\frac{3}{4}y to get -\frac{27}{4}y.

$$-\frac{27}{4}y-\frac{5}{3}=-\frac{5}{4}$$

Add \frac{5}{3} to both sides.

$$-\frac{27}{4}y=-\frac{5}{4}+\frac{5}{3}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{5}{4} and \frac{5}{3} to fractions with denominator 12.

$$-\frac{27}{4}y=-\frac{15}{12}+\frac{20}{12}$$

Since -\frac{15}{12} and \frac{20}{12} have the same denominator, add them by adding their numerators.

$$-\frac{27}{4}y=\frac{-15+20}{12}$$

Add -15 and 20 to get 5.

$$-\frac{27}{4}y=\frac{5}{12}$$

Multiply both sides by -\frac{4}{27}, the reciprocal of -\frac{27}{4}.

$$y=\frac{5}{12}\left(-\frac{4}{27}\right)$$

Multiply \frac{5}{12} times -\frac{4}{27} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{5\left(-4\right)}{12\times 27}$$

Do the multiplications in the fraction \frac{5\left(-4\right)}{12\times 27}.

$$y=\frac{-20}{324}$$

Reduce the fraction \frac{-20}{324} to lowest terms by extracting and canceling out 4.

$$y=-\frac{5}{81}$$