Solve -2x+5/2=-5/2x-7/3

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

Solve for x

$$x = -\frac{29}{3} = -9\frac{2}{3} \approx -9.666666667$$

Steps for Solving Linear Equation

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

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

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

$$\frac{1}{2}x+\frac{5}{2}=-\frac{7}{3}$$

Subtract \frac{5}{2} from both sides.

$$\frac{1}{2}x=-\frac{7}{3}-\frac{5}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{7}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{1}{2}x=-\frac{14}{6}-\frac{15}{6}$$

Since -\frac{14}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{-14-15}{6}$$

Subtract 15 from -14 to get -29.

$$\frac{1}{2}x=-\frac{29}{6}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=-\frac{29}{6}\times 2$$

Express -\frac{29}{6}\times 2 as a single fraction.

$$x=\frac{-29\times 2}{6}$$

Multiply -29 and 2 to get -58.

$$x=\frac{-58}{6}$$

Reduce the fraction \frac{-58}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{29}{3}$$