Solve 1/5x-3=5*left(1/10x+1/10right)

$$\frac{ 1 }{ 5 } x-3 = 5 \times \left( \frac{ 1 }{ 10 } x+ \frac{ 1 }{ 10 } \right)$$

Solve for x

$$x = -\frac{35}{3} = -11\frac{2}{3} \approx -11.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by \frac{1}{10}x+\frac{1}{10}.

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

Multiply 5 and \frac{1}{10} to get \frac{5}{10}.

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

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{5}x-3=\frac{1}{2}x+5\times \frac{1}{10}$$

Multiply 5 and \frac{1}{10} to get \frac{5}{10}.

$$\frac{1}{5}x-3=\frac{1}{2}x+\frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{5}x-3=\frac{1}{2}x+\frac{1}{2}$$

Subtract \frac{1}{2}x from both sides.

$$\frac{1}{5}x-3-\frac{1}{2}x=\frac{1}{2}$$

Combine \frac{1}{5}x and -\frac{1}{2}x to get -\frac{3}{10}x.

$$-\frac{3}{10}x-3=\frac{1}{2}$$

Add 3 to both sides.

$$-\frac{3}{10}x=\frac{1}{2}+3$$

Convert 3 to fraction \frac{6}{2}.

$$-\frac{3}{10}x=\frac{1}{2}+\frac{6}{2}$$

Since \frac{1}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$-\frac{3}{10}x=\frac{1+6}{2}$$

Add 1 and 6 to get 7.

$$-\frac{3}{10}x=\frac{7}{2}$$

Multiply both sides by -\frac{10}{3}, the reciprocal of -\frac{3}{10}.

$$x=\frac{7}{2}\left(-\frac{10}{3}\right)$$

Multiply \frac{7}{2} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\left(-10\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{7\left(-10\right)}{2\times 3}.

$$x=\frac{-70}{6}$$

Reduce the fraction \frac{-70}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{35}{3}$$