Solve 31/2/2-21/3y=31/4

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

Solve for y

$$y=-\frac{9}{14}\approx -0.642857143$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$6\times \frac{3\times 2+1}{2}-4\left(2\times 3+1\right)y=3\left(3\times 4+1\right)$$

Multiply 3 and 2 to get 6.

$$6\times \frac{6+1}{2}-4\left(2\times 3+1\right)y=3\left(3\times 4+1\right)$$

Add 6 and 1 to get 7.

$$6\times \frac{7}{2}-4\left(2\times 3+1\right)y=3\left(3\times 4+1\right)$$

Express 6\times \frac{7}{2} as a single fraction.

$$\frac{6\times 7}{2}-4\left(2\times 3+1\right)y=3\left(3\times 4+1\right)$$

Multiply 6 and 7 to get 42.

$$\frac{42}{2}-4\left(2\times 3+1\right)y=3\left(3\times 4+1\right)$$

Divide 42 by 2 to get 21.

$$21-4\left(2\times 3+1\right)y=3\left(3\times 4+1\right)$$

Multiply 2 and 3 to get 6.

$$21-4\left(6+1\right)y=3\left(3\times 4+1\right)$$

Add 6 and 1 to get 7.

$$21-4\times 7y=3\left(3\times 4+1\right)$$

Multiply 4 and 7 to get 28.

$$21-28y=3\left(3\times 4+1\right)$$

Multiply 3 and 4 to get 12.

$$21-28y=3\left(12+1\right)$$

Add 12 and 1 to get 13.

$$21-28y=3\times 13$$

Multiply 3 and 13 to get 39.

$$21-28y=39$$

Subtract 21 from both sides.

$$-28y=39-21$$

Subtract 21 from 39 to get 18.

$$-28y=18$$

Divide both sides by -28.

$$y=\frac{18}{-28}$$

Reduce the fraction \frac{18}{-28} to lowest terms by extracting and canceling out 2.

$$y=-\frac{9}{14}$$