Solve -5/2y+1/2=-2/5y-5

$$- \frac { 5 } { 2 } y + \frac { 1 } { 2 } = - \frac { 2 } { 5 } y - 5$$

Solve for y

$$y = \frac{55}{21} = 2\frac{13}{21} \approx 2.619047619$$

Steps for Solving Linear Equation

Add \frac{2}{5}y to both sides.

$$-\frac{5}{2}y+\frac{1}{2}+\frac{2}{5}y=-5$$

Combine -\frac{5}{2}y and \frac{2}{5}y to get -\frac{21}{10}y.

$$-\frac{21}{10}y+\frac{1}{2}=-5$$

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

$$-\frac{21}{10}y=-5-\frac{1}{2}$$

Convert -5 to fraction -\frac{10}{2}.

$$-\frac{21}{10}y=-\frac{10}{2}-\frac{1}{2}$$

Since -\frac{10}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{21}{10}y=\frac{-10-1}{2}$$

Subtract 1 from -10 to get -11.

$$-\frac{21}{10}y=-\frac{11}{2}$$

Multiply both sides by -\frac{10}{21}, the reciprocal of -\frac{21}{10}.

$$y=-\frac{11}{2}\left(-\frac{10}{21}\right)$$

Multiply -\frac{11}{2} times -\frac{10}{21} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-11\left(-10\right)}{2\times 21}$$

Do the multiplications in the fraction \frac{-11\left(-10\right)}{2\times 21}.

$$y=\frac{110}{42}$$

Reduce the fraction \frac{110}{42} to lowest terms by extracting and canceling out 2.

$$y=\frac{55}{21}$$