Solve 10-5/y+5/28=5/8+30-3/27

$$\frac { 10 - 5 } { y } + \frac { 5 } { 28 } = \frac { 5 } { 8 } + \frac { 30 - 3 } { 27 }$$

Solve for y

$$y = \frac{280}{81} = 3\frac{37}{81} \approx 3.456790123$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1512y, the least common multiple of y,28,8,27.

$$1512\left(10-5\right)+1512y\times \frac{5}{28}=1512y\times \frac{5}{8}+56y\left(30-3\right)$$

Subtract 5 from 10 to get 5.

$$1512\times 5+1512y\times \frac{5}{28}=1512y\times \frac{5}{8}+56y\left(30-3\right)$$

Multiply 1512 and 5 to get 7560.

$$7560+1512y\times \frac{5}{28}=1512y\times \frac{5}{8}+56y\left(30-3\right)$$

Express 1512\times \frac{5}{28} as a single fraction.

$$7560+\frac{1512\times 5}{28}y=1512y\times \frac{5}{8}+56y\left(30-3\right)$$

Multiply 1512 and 5 to get 7560.

$$7560+\frac{7560}{28}y=1512y\times \frac{5}{8}+56y\left(30-3\right)$$

Divide 7560 by 28 to get 270.

$$7560+270y=1512y\times \frac{5}{8}+56y\left(30-3\right)$$

Express 1512\times \frac{5}{8} as a single fraction.

$$7560+270y=\frac{1512\times 5}{8}y+56y\left(30-3\right)$$

Multiply 1512 and 5 to get 7560.

$$7560+270y=\frac{7560}{8}y+56y\left(30-3\right)$$

Divide 7560 by 8 to get 945.

$$7560+270y=945y+56y\left(30-3\right)$$

Subtract 3 from 30 to get 27.

$$7560+270y=945y+56y\times 27$$

Multiply 56 and 27 to get 1512.

$$7560+270y=945y+1512y$$

Combine 945y and 1512y to get 2457y.

$$7560+270y=2457y$$

Subtract 2457y from both sides.

$$7560+270y-2457y=0$$

Combine 270y and -2457y to get -2187y.

$$7560-2187y=0$$

Subtract 7560 from both sides. Anything subtracted from zero gives its negation.

$$-2187y=-7560$$

Divide both sides by -2187.

$$y=\frac{-7560}{-2187}$$

Reduce the fraction \frac{-7560}{-2187} to lowest terms by extracting and canceling out -27.

$$y=\frac{280}{81}$$