Solve -5/3x-5/2=1/2x-7

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

Solve for x

$$x = \frac{27}{13} = 2\frac{1}{13} \approx 2.076923077$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

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

Combine -\frac{5}{3}x and -\frac{1}{2}x to get -\frac{13}{6}x.

$$-\frac{13}{6}x-\frac{5}{2}=-7$$

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

$$-\frac{13}{6}x=-7+\frac{5}{2}$$

Convert -7 to fraction -\frac{14}{2}.

$$-\frac{13}{6}x=-\frac{14}{2}+\frac{5}{2}$$

Since -\frac{14}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$-\frac{13}{6}x=\frac{-14+5}{2}$$

Add -14 and 5 to get -9.

$$-\frac{13}{6}x=-\frac{9}{2}$$

Multiply both sides by -\frac{6}{13}, the reciprocal of -\frac{13}{6}.

$$x=-\frac{9}{2}\left(-\frac{6}{13}\right)$$

Multiply -\frac{9}{2} times -\frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\left(-6\right)}{2\times 13}$$

Do the multiplications in the fraction \frac{-9\left(-6\right)}{2\times 13}.

$$x=\frac{54}{26}$$

Reduce the fraction \frac{54}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{27}{13}$$