Solve 2y/3-y-4/2=5(2y-1)/4

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

Solve for y

$$y = \frac{39}{28} = 1\frac{11}{28} \approx 1.392857143$$

Steps for Solving Linear Equation

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

$$4\times 2y-6\left(y-4\right)=3\times 5\left(2y-1\right)$$

Multiply 4 and 2 to get 8.

$$8y-6\left(y-4\right)=3\times 5\left(2y-1\right)$$

Use the distributive property to multiply -6 by y-4.

$$8y-6y+24=3\times 5\left(2y-1\right)$$

Combine 8y and -6y to get 2y.

$$2y+24=3\times 5\left(2y-1\right)$$

Multiply 3 and 5 to get 15.

$$2y+24=15\left(2y-1\right)$$

Use the distributive property to multiply 15 by 2y-1.

$$2y+24=30y-15$$

Subtract 30y from both sides.

$$2y+24-30y=-15$$

Combine 2y and -30y to get -28y.

$$-28y+24=-15$$

Subtract 24 from both sides.

$$-28y=-15-24$$

Subtract 24 from -15 to get -39.

$$-28y=-39$$

Divide both sides by -28.

$$y=\frac{-39}{-28}$$

Fraction \frac{-39}{-28} can be simplified to \frac{39}{28} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{39}{28}$$