Solve 0.2left(6x+1right)/3*6=0.5x/-9

$$\frac{ 0.2 \left( 6x+1 \right) }{ 3 \cdot 6 } = \frac{ 0.5x }{ -9 }$$

Solve for x

$$x=-\frac{1}{11}\approx -0.090909091$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -9.

$$-\frac{1}{2}\times 0.2\left(6x+1\right)=0.5x$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}\times \frac{1}{5}\left(6x+1\right)=0.5x$$

Multiply -\frac{1}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{2\times 5}\left(6x+1\right)=0.5x$$

Do the multiplications in the fraction \frac{-1}{2\times 5}.

$$\frac{-1}{10}\left(6x+1\right)=0.5x$$

Fraction \frac{-1}{10} can be rewritten as -\frac{1}{10} by extracting the negative sign.

$$-\frac{1}{10}\left(6x+1\right)=0.5x$$

Use the distributive property to multiply -\frac{1}{10} by 6x+1.

$$-\frac{1}{10}\times 6x-\frac{1}{10}=0.5x$$

Express -\frac{1}{10}\times 6 as a single fraction.

$$\frac{-6}{10}x-\frac{1}{10}=0.5x$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{5}x-\frac{1}{10}=0.5x$$

Subtract 0.5x from both sides.

$$-\frac{3}{5}x-\frac{1}{10}-0.5x=0$$

Combine -\frac{3}{5}x and -0.5x to get -\frac{11}{10}x.

$$-\frac{11}{10}x-\frac{1}{10}=0$$

Add \frac{1}{10} to both sides. Anything plus zero gives itself.

$$-\frac{11}{10}x=\frac{1}{10}$$

Multiply both sides by -\frac{10}{11}, the reciprocal of -\frac{11}{10}.

$$x=\frac{1}{10}\left(-\frac{10}{11}\right)$$

Multiply \frac{1}{10} times -\frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-10\right)}{10\times 11}$$

Do the multiplications in the fraction \frac{1\left(-10\right)}{10\times 11}.

$$x=\frac{-10}{110}$$

Reduce the fraction \frac{-10}{110} to lowest terms by extracting and canceling out 10.

$$x=-\frac{1}{11}$$