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

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

Solve for u

$$u = -\frac{17}{7} = -2\frac{3}{7} \approx -2.428571429$$

Steps for Solving Linear Equation

Combine \frac{5}{4}u and -\frac{2}{3}u to get \frac{7}{12}u.

$$\frac{7}{12}u=\frac{-3}{4}-\frac{2}{3}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{7}{12}u=-\frac{3}{4}-\frac{2}{3}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{7}{12}u=-\frac{9}{12}-\frac{8}{12}$$

Since -\frac{9}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{12}u=\frac{-9-8}{12}$$

Subtract 8 from -9 to get -17.

$$\frac{7}{12}u=-\frac{17}{12}$$

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

$$u=-\frac{17}{12}\times \frac{12}{7}$$

Multiply -\frac{17}{12} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-17\times 12}{12\times 7}$$

Cancel out 12 in both numerator and denominator.

$$u=\frac{-17}{7}$$

Fraction \frac{-17}{7} can be rewritten as -\frac{17}{7} by extracting the negative sign.

$$u=-\frac{17}{7}$$