Solve 1/5x-1/2=-7x-1/5

$$\frac{ 1 }{ 5 } x- \frac{ 1 }{ 2 } =-7x- \frac{ 1 }{ 5 }$$

Solve for x

$$x=\frac{1}{24}\approx 0.041666667$$

Steps for Solving Linear Equation

Add 7x to both sides.

$$\frac{1}{5}x-\frac{1}{2}+7x=-\frac{1}{5}$$

Combine \frac{1}{5}x and 7x to get \frac{36}{5}x.

$$\frac{36}{5}x-\frac{1}{2}=-\frac{1}{5}$$

Add \frac{1}{2} to both sides.

$$\frac{36}{5}x=-\frac{1}{5}+\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{1}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{36}{5}x=-\frac{2}{10}+\frac{5}{10}$$

Since -\frac{2}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{36}{5}x=\frac{-2+5}{10}$$

Add -2 and 5 to get 3.

$$\frac{36}{5}x=\frac{3}{10}$$

Multiply both sides by \frac{5}{36}, the reciprocal of \frac{36}{5}.

$$x=\frac{3}{10}\times \frac{5}{36}$$

Multiply \frac{3}{10} times \frac{5}{36} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\times 5}{10\times 36}$$

Do the multiplications in the fraction \frac{3\times 5}{10\times 36}.

$$x=\frac{15}{360}$$

Reduce the fraction \frac{15}{360} to lowest terms by extracting and canceling out 15.

$$x=\frac{1}{24}$$