Solve 1/3+5/4x=3/4+2/3x

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

Solve for x

$$x=\frac{5}{7}\approx 0.714285714$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}x from both sides.

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

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

$$\frac{1}{3}+\frac{7}{12}x=\frac{3}{4}$$

Subtract \frac{1}{3} from both sides.

$$\frac{7}{12}x=\frac{3}{4}-\frac{1}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{7}{12}x=\frac{9}{12}-\frac{4}{12}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{12}x=\frac{9-4}{12}$$

Subtract 4 from 9 to get 5.

$$\frac{7}{12}x=\frac{5}{12}$$

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

$$x=\frac{5}{12}\times \frac{12}{7}$$

Multiply \frac{5}{12} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 12}{12\times 7}$$

Cancel out 12 in both numerator and denominator.

$$x=\frac{5}{7}$$