Solve -3/2u-5=3/4u+1/3

$$- \frac { 3 } { 2 } u - 5 = \frac { 3 } { 4 } u + \frac { 1 } { 3 }$$

Solve for u

$$u = -\frac{64}{27} = -2\frac{10}{27} \approx -2.37037037$$

Steps for Solving Linear Equation

Subtract \frac{3}{4}u from both sides.

$$-\frac{3}{2}u-5-\frac{3}{4}u=\frac{1}{3}$$

Combine -\frac{3}{2}u and -\frac{3}{4}u to get -\frac{9}{4}u.

$$-\frac{9}{4}u-5=\frac{1}{3}$$

Add 5 to both sides.

$$-\frac{9}{4}u=\frac{1}{3}+5$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{9}{4}u=\frac{1}{3}+\frac{15}{3}$$

Since \frac{1}{3} and \frac{15}{3} have the same denominator, add them by adding their numerators.

$$-\frac{9}{4}u=\frac{1+15}{3}$$

Add 1 and 15 to get 16.

$$-\frac{9}{4}u=\frac{16}{3}$$

Multiply both sides by -\frac{4}{9}, the reciprocal of -\frac{9}{4}.

$$u=\frac{16}{3}\left(-\frac{4}{9}\right)$$

Multiply \frac{16}{3} times -\frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{16\left(-4\right)}{3\times 9}$$

Do the multiplications in the fraction \frac{16\left(-4\right)}{3\times 9}.

$$u=\frac{-64}{27}$$

Fraction \frac{-64}{27} can be rewritten as -\frac{64}{27} by extracting the negative sign.

$$u=-\frac{64}{27}$$