Solve 6-10y/-12=1/5-5y/2

$$\frac { 6 - 10 y } { - 12 } = \frac { \frac { 1 } { 5 } - 5 y } { 2 }$$

Solve for y

$$y=\frac{9}{50}=0.18$$

Steps for Solving Linear Equation

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

$$-\left(6-10y\right)=6\left(\frac{1}{5}-5y\right)$$

To find the opposite of 6-10y, find the opposite of each term.

$$-6-\left(-10y\right)=6\left(\frac{1}{5}-5y\right)$$

The opposite of -10y is 10y.

$$-6+10y=6\left(\frac{1}{5}-5y\right)$$

Use the distributive property to multiply 6 by \frac{1}{5}-5y.

$$-6+10y=6\times \frac{1}{5}-30y$$

Multiply 6 and \frac{1}{5} to get \frac{6}{5}.

$$-6+10y=\frac{6}{5}-30y$$

Add 30y to both sides.

$$-6+10y+30y=\frac{6}{5}$$

Combine 10y and 30y to get 40y.

$$-6+40y=\frac{6}{5}$$

Add 6 to both sides.

$$40y=\frac{6}{5}+6$$

Convert 6 to fraction \frac{30}{5}.

$$40y=\frac{6}{5}+\frac{30}{5}$$

Since \frac{6}{5} and \frac{30}{5} have the same denominator, add them by adding their numerators.

$$40y=\frac{6+30}{5}$$

Add 6 and 30 to get 36.

$$40y=\frac{36}{5}$$

Divide both sides by 40.

$$y=\frac{\frac{36}{5}}{40}$$

Express \frac{\frac{36}{5}}{40} as a single fraction.

$$y=\frac{36}{5\times 40}$$

Multiply 5 and 40 to get 200.

$$y=\frac{36}{200}$$

Reduce the fraction \frac{36}{200} to lowest terms by extracting and canceling out 4.

$$y=\frac{9}{50}$$