Solve -5/2x+2/3=-5/3x-3

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

Solve for x

$$x = \frac{22}{5} = 4\frac{2}{5} = 4.4$$

Steps for Solving Linear Equation

Add \frac{5}{3}x to both sides.

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

Combine -\frac{5}{2}x and \frac{5}{3}x to get -\frac{5}{6}x.

$$-\frac{5}{6}x+\frac{2}{3}=-3$$

Subtract \frac{2}{3} from both sides.

$$-\frac{5}{6}x=-3-\frac{2}{3}$$

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

$$-\frac{5}{6}x=-\frac{9}{3}-\frac{2}{3}$$

Since -\frac{9}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{6}x=\frac{-9-2}{3}$$

Subtract 2 from -9 to get -11.

$$-\frac{5}{6}x=-\frac{11}{3}$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}.

$$x=-\frac{11}{3}\left(-\frac{6}{5}\right)$$

Multiply -\frac{11}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\left(-6\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{-11\left(-6\right)}{3\times 5}.

$$x=\frac{66}{15}$$

Reduce the fraction \frac{66}{15} to lowest terms by extracting and canceling out 3.

$$x=\frac{22}{5}$$