Solve 5/3-5/4x=25/12-2/3x+frac{3}{4}

$$\frac { 5 } { 3 } - \frac { 5 } { 4 } x = \frac { 25 } { 12 } - \frac { 2 } { 3 } x + \frac { 3 } { 4 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Least common multiple of 12 and 4 is 12. Convert \frac{25}{12} and \frac{3}{4} to fractions with denominator 12.

$$\frac{5}{3}-\frac{5}{4}x=\frac{25}{12}-\frac{2}{3}x+\frac{9}{12}$$

Since \frac{25}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}-\frac{5}{4}x=\frac{25+9}{12}-\frac{2}{3}x$$

Add 25 and 9 to get 34.

$$\frac{5}{3}-\frac{5}{4}x=\frac{34}{12}-\frac{2}{3}x$$

Reduce the fraction \frac{34}{12} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}-\frac{5}{4}x=\frac{17}{6}-\frac{2}{3}x$$

Add \frac{2}{3}x to both sides.

$$\frac{5}{3}-\frac{5}{4}x+\frac{2}{3}x=\frac{17}{6}$$

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

$$\frac{5}{3}-\frac{7}{12}x=\frac{17}{6}$$

Subtract \frac{5}{3} from both sides.

$$-\frac{7}{12}x=\frac{17}{6}-\frac{5}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{17}{6} and \frac{5}{3} to fractions with denominator 6.

$$-\frac{7}{12}x=\frac{17}{6}-\frac{10}{6}$$

Since \frac{17}{6} and \frac{10}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{12}x=\frac{17-10}{6}$$

Subtract 10 from 17 to get 7.

$$-\frac{7}{12}x=\frac{7}{6}$$

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

$$x=\frac{7}{6}\left(-\frac{12}{7}\right)$$

Multiply \frac{7}{6} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\left(-12\right)}{6\times 7}$$

Cancel out 7 in both numerator and denominator.

$$x=\frac{-12}{6}$$

Divide -12 by 6 to get -2.

$$x=-2$$