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

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

Solve for x

$$x=\frac{39}{68}\approx 0.573529412$$

Steps for Solving Linear Equation

Add \frac{1}{5}x to both sides.

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

Combine -7x and \frac{1}{5}x to get -\frac{34}{5}x.

$$-\frac{34}{5}x+\frac{5}{2}=-\frac{7}{5}$$

Subtract \frac{5}{2} from both sides.

$$-\frac{34}{5}x=-\frac{7}{5}-\frac{5}{2}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{7}{5} and \frac{5}{2} to fractions with denominator 10.

$$-\frac{34}{5}x=-\frac{14}{10}-\frac{25}{10}$$

Since -\frac{14}{10} and \frac{25}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{34}{5}x=\frac{-14-25}{10}$$

Subtract 25 from -14 to get -39.

$$-\frac{34}{5}x=-\frac{39}{10}$$

Multiply both sides by -\frac{5}{34}, the reciprocal of -\frac{34}{5}.

$$x=-\frac{39}{10}\left(-\frac{5}{34}\right)$$

Multiply -\frac{39}{10} times -\frac{5}{34} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-39\left(-5\right)}{10\times 34}$$

Do the multiplications in the fraction \frac{-39\left(-5\right)}{10\times 34}.

$$x=\frac{195}{340}$$

Reduce the fraction \frac{195}{340} to lowest terms by extracting and canceling out 5.

$$x=\frac{39}{68}$$