Solve 2y-1/5=13/4-2-y/2

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

Solve for y

$$y = -\frac{19}{2} = -9\frac{1}{2} = -9.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4,2.

$$4\left(2y-1\right)=5\left(1\times 4+3\right)-10\left(2-y\right)$$

Use the distributive property to multiply 4 by 2y-1.

$$8y-4=5\left(1\times 4+3\right)-10\left(2-y\right)$$

Multiply 1 and 4 to get 4.

$$8y-4=5\left(4+3\right)-10\left(2-y\right)$$

Add 4 and 3 to get 7.

$$8y-4=5\times 7-10\left(2-y\right)$$

Multiply 5 and 7 to get 35.

$$8y-4=35-10\left(2-y\right)$$

Use the distributive property to multiply -10 by 2-y.

$$8y-4=35-20+10y$$

Subtract 20 from 35 to get 15.

$$8y-4=15+10y$$

Subtract 10y from both sides.

$$8y-4-10y=15$$

Combine 8y and -10y to get -2y.

$$-2y-4=15$$

Add 4 to both sides.

$$-2y=15+4$$

Add 15 and 4 to get 19.

$$-2y=19$$

Divide both sides by -2.

$$y=\frac{19}{-2}$$

Fraction \frac{19}{-2} can be rewritten as -\frac{19}{2} by extracting the negative sign.

$$y=-\frac{19}{2}$$