Solve 2x-3/4=1/3x+5/6

$$2 x - \frac { 3 } { 4 } = \frac { 1 } { 3 } x + \frac { 5 } { 6 }$$

Solve for x

$$x=\frac{19}{20}=0.95$$

Steps for Solving Linear Equation

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

$$2x-\frac{3}{4}-\frac{1}{3}x=\frac{5}{6}$$

Combine 2x and -\frac{1}{3}x to get \frac{5}{3}x.

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

Add \frac{3}{4} to both sides.

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

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{5}{3}x=\frac{10}{12}+\frac{9}{12}$$

Since \frac{10}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}x=\frac{10+9}{12}$$

Add 10 and 9 to get 19.

$$\frac{5}{3}x=\frac{19}{12}$$

Multiply both sides by \frac{3}{5}, the reciprocal of \frac{5}{3}.

$$x=\frac{19}{12}\times \frac{3}{5}$$

Multiply \frac{19}{12} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\times 3}{12\times 5}$$

Do the multiplications in the fraction \frac{19\times 3}{12\times 5}.

$$x=\frac{57}{60}$$

Reduce the fraction \frac{57}{60} to lowest terms by extracting and canceling out 3.

$$x=\frac{19}{20}$$