Solve -1/3x-2/3=4/3x-9

$$- \frac { 1 } { 3 } x - \frac { 2 } { 3 } = \frac { 4 } { 3 } x - 9$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Subtract \frac{4}{3}x from both sides.

$$-\frac{1}{3}x-\frac{2}{3}-\frac{4}{3}x=-9$$

Combine -\frac{1}{3}x and -\frac{4}{3}x to get -\frac{5}{3}x.

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

Add \frac{2}{3} to both sides.

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

Convert -9 to fraction -\frac{27}{3}.

$$-\frac{5}{3}x=-\frac{27}{3}+\frac{2}{3}$$

Since -\frac{27}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$-\frac{5}{3}x=\frac{-27+2}{3}$$

Add -27 and 2 to get -25.

$$-\frac{5}{3}x=-\frac{25}{3}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$x=-\frac{25}{3}\left(-\frac{3}{5}\right)$$

Multiply -\frac{25}{3} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-25\left(-3\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{-25\left(-3\right)}{3\times 5}.

$$x=\frac{75}{15}$$

Divide 75 by 15 to get 5.

$$x=5$$