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

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

Solve for u

$$u = -\frac{16}{7} = -2\frac{2}{7} \approx -2.285714286$$

Steps for Solving Linear Equation

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

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

Combine -\frac{4}{3}u and \frac{5}{2}u to get \frac{7}{6}u.

$$\frac{7}{6}u+1=-\frac{5}{3}$$

Subtract 1 from both sides.

$$\frac{7}{6}u=-\frac{5}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{7}{6}u=-\frac{5}{3}-\frac{3}{3}$$

Since -\frac{5}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}u=\frac{-5-3}{3}$$

Subtract 3 from -5 to get -8.

$$\frac{7}{6}u=-\frac{8}{3}$$

Multiply both sides by \frac{6}{7}, the reciprocal of \frac{7}{6}.

$$u=-\frac{8}{3}\times \frac{6}{7}$$

Multiply -\frac{8}{3} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-8\times 6}{3\times 7}$$

Do the multiplications in the fraction \frac{-8\times 6}{3\times 7}.

$$u=\frac{-48}{21}$$

Reduce the fraction \frac{-48}{21} to lowest terms by extracting and canceling out 3.

$$u=-\frac{16}{7}$$