Solve -2/3x+5/3=-2/5x-6

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

Solve for x

$$x = \frac{115}{4} = 28\frac{3}{4} = 28.75$$

Steps for Solving Linear Equation

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

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

Combine -\frac{2}{3}x and \frac{2}{5}x to get -\frac{4}{15}x.

$$-\frac{4}{15}x+\frac{5}{3}=-6$$

Subtract \frac{5}{3} from both sides.

$$-\frac{4}{15}x=-6-\frac{5}{3}$$

Convert -6 to fraction -\frac{18}{3}.

$$-\frac{4}{15}x=-\frac{18}{3}-\frac{5}{3}$$

Since -\frac{18}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{15}x=\frac{-18-5}{3}$$

Subtract 5 from -18 to get -23.

$$-\frac{4}{15}x=-\frac{23}{3}$$

Multiply both sides by -\frac{15}{4}, the reciprocal of -\frac{4}{15}.

$$x=-\frac{23}{3}\left(-\frac{15}{4}\right)$$

Multiply -\frac{23}{3} times -\frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-23\left(-15\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{-23\left(-15\right)}{3\times 4}.

$$x=\frac{345}{12}$$

Reduce the fraction \frac{345}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{115}{4}$$