Solve -5/2y+3=-1/2y-5/3

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

Solve for y

$$y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps for Solving Linear Equation

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

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

Combine -\frac{5}{2}y and \frac{1}{2}y to get -2y.

$$-2y+3=-\frac{5}{3}$$

Subtract 3 from both sides.

$$-2y=-\frac{5}{3}-3$$

Convert 3 to fraction \frac{9}{3}.

$$-2y=-\frac{5}{3}-\frac{9}{3}$$

Since -\frac{5}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$-2y=\frac{-5-9}{3}$$

Subtract 9 from -5 to get -14.

$$-2y=-\frac{14}{3}$$

Divide both sides by -2.

$$y=\frac{-\frac{14}{3}}{-2}$$

Express \frac{-\frac{14}{3}}{-2} as a single fraction.

$$y=\frac{-14}{3\left(-2\right)}$$

Multiply 3 and -2 to get -6.

$$y=\frac{-14}{-6}$$

Reduce the fraction \frac{-14}{-6} to lowest terms by extracting and canceling out -2.

$$y=\frac{7}{3}$$