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

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

Solve for x

$$x=-\frac{2}{5}=-0.4$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}x from both sides.

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

Combine -\frac{1}{2}x and -\frac{1}{3}x to get -\frac{5}{6}x.

$$-\frac{5}{6}x-1=-\frac{2}{3}$$

Add 1 to both sides.

$$-\frac{5}{6}x=-\frac{2}{3}+1$$

Convert 1 to fraction \frac{3}{3}.

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

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

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

Add -2 and 3 to get 1.

$$-\frac{5}{6}x=\frac{1}{3}$$

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

$$x=\frac{1}{3}\left(-\frac{6}{5}\right)$$

Multiply \frac{1}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-6\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{1\left(-6\right)}{3\times 5}.

$$x=\frac{-6}{15}$$

Reduce the fraction \frac{-6}{15} to lowest terms by extracting and canceling out 3.

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