Solve -3/2u-3/4=2/3u-7

$$- \frac { 3 } { 2 } u - \frac { 3 } { 4 } = \frac { 2 } { 3 } u - 7$$

Solve for u

$$u = \frac{75}{26} = 2\frac{23}{26} \approx 2.884615385$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}u from both sides.

$$-\frac{3}{2}u-\frac{3}{4}-\frac{2}{3}u=-7$$

Combine -\frac{3}{2}u and -\frac{2}{3}u to get -\frac{13}{6}u.

$$-\frac{13}{6}u-\frac{3}{4}=-7$$

Add \frac{3}{4} to both sides.

$$-\frac{13}{6}u=-7+\frac{3}{4}$$

Convert -7 to fraction -\frac{28}{4}.

$$-\frac{13}{6}u=-\frac{28}{4}+\frac{3}{4}$$

Since -\frac{28}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$-\frac{13}{6}u=\frac{-28+3}{4}$$

Add -28 and 3 to get -25.

$$-\frac{13}{6}u=-\frac{25}{4}$$

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

$$u=-\frac{25}{4}\left(-\frac{6}{13}\right)$$

Multiply -\frac{25}{4} times -\frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-25\left(-6\right)}{4\times 13}$$

Do the multiplications in the fraction \frac{-25\left(-6\right)}{4\times 13}.

$$u=\frac{150}{52}$$

Reduce the fraction \frac{150}{52} to lowest terms by extracting and canceling out 2.

$$u=\frac{75}{26}$$