Solve -1/6y+5/6=1/4y-5/4

$$- \frac { 1 } { 6 } y + \frac { 5 } { 6 } = \frac { 1 } { 4 } y - \frac { 5 } { 4 }$$

Solve for y

$$y=5$$

Steps for Solving Linear Equation

Subtract \frac{1}{4}y from both sides.

$$-\frac{1}{6}y+\frac{5}{6}-\frac{1}{4}y=-\frac{5}{4}$$

Combine -\frac{1}{6}y and -\frac{1}{4}y to get -\frac{5}{12}y.

$$-\frac{5}{12}y+\frac{5}{6}=-\frac{5}{4}$$

Subtract \frac{5}{6} from both sides.

$$-\frac{5}{12}y=-\frac{5}{4}-\frac{5}{6}$$

Least common multiple of 4 and 6 is 12. Convert -\frac{5}{4} and \frac{5}{6} to fractions with denominator 12.

$$-\frac{5}{12}y=-\frac{15}{12}-\frac{10}{12}$$

Since -\frac{15}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{12}y=\frac{-15-10}{12}$$

Subtract 10 from -15 to get -25.

$$-\frac{5}{12}y=-\frac{25}{12}$$

Multiply both sides by -\frac{12}{5}, the reciprocal of -\frac{5}{12}.

$$y=-\frac{25}{12}\left(-\frac{12}{5}\right)$$

Multiply -\frac{25}{12} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-25\left(-12\right)}{12\times 5}$$

Do the multiplications in the fraction \frac{-25\left(-12\right)}{12\times 5}.

$$y=\frac{300}{60}$$

Divide 300 by 60 to get 5.

$$y=5$$