Solve 1/3(1/2-2y)+11/2y=1/6

$$\frac { 1 } { 3 } ( \frac { 1 } { 2 } - 2 y ) + 1 \frac { 1 } { 2 } y = \frac { 1 } { 6 }$$

Solve for y

$$y=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2,6.

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

Use the distributive property to multiply 2 by \frac{1}{2}-2y.

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

Cancel out 2 and 2.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$1-4y+3\times 3y=1$$

Multiply 3 and 3 to get 9.

$$1-4y+9y=1$$

Combine -4y and 9y to get 5y.

$$1+5y=1$$

Subtract 1 from both sides.

$$5y=1-1$$

Subtract 1 from 1 to get 0.

$$5y=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 5 is not equal to 0, y must be equal to 0.

$$y=0$$