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

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

Solve for u

$$u = \frac{75}{7} = 10\frac{5}{7} \approx 10.714285714$$

Steps for Solving Linear Equation

Add \frac{1}{4}u to both sides.

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

Combine \frac{1}{3}u and \frac{1}{4}u to get \frac{7}{12}u.

$$\frac{7}{12}u-\frac{5}{4}=5$$

Add \frac{5}{4} to both sides.

$$\frac{7}{12}u=5+\frac{5}{4}$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{7}{12}u=\frac{20}{4}+\frac{5}{4}$$

Since \frac{20}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}u=\frac{20+5}{4}$$

Add 20 and 5 to get 25.

$$\frac{7}{12}u=\frac{25}{4}$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$u=\frac{25}{4}\times \frac{12}{7}$$

Multiply \frac{25}{4} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{25\times 12}{4\times 7}$$

Do the multiplications in the fraction \frac{25\times 12}{4\times 7}.

$$u=\frac{300}{28}$$

Reduce the fraction \frac{300}{28} to lowest terms by extracting and canceling out 4.

$$u=\frac{75}{7}$$