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

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

Solve for x

$$x=-\frac{11}{21}\approx -0.523809524$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

Combine -\frac{5}{2}x and -x to get -\frac{7}{2}x.

$$-\frac{7}{2}x-\frac{5}{2}=-\frac{2}{3}$$

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

$$-\frac{7}{2}x=-\frac{2}{3}+\frac{5}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{5}{2} to fractions with denominator 6.

$$-\frac{7}{2}x=-\frac{4}{6}+\frac{15}{6}$$

Since -\frac{4}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$-\frac{7}{2}x=\frac{-4+15}{6}$$

Add -4 and 15 to get 11.

$$-\frac{7}{2}x=\frac{11}{6}$$

Multiply both sides by -\frac{2}{7}, the reciprocal of -\frac{7}{2}.

$$x=\frac{11}{6}\left(-\frac{2}{7}\right)$$

Multiply \frac{11}{6} times -\frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\left(-2\right)}{6\times 7}$$

Do the multiplications in the fraction \frac{11\left(-2\right)}{6\times 7}.

$$x=\frac{-22}{42}$$

Reduce the fraction \frac{-22}{42} to lowest terms by extracting and canceling out 2.

$$x=-\frac{11}{21}$$