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

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

Solve for x

$$x = \frac{14}{3} = 4\frac{2}{3} \approx 4.666666667$$

Steps for Solving Linear Equation

Add x to both sides.

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

Combine -\frac{3}{4}x and x to get \frac{1}{4}x.

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

Subtract \frac{5}{6} from both sides.

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

Convert 2 to fraction \frac{12}{6}.

$$\frac{1}{4}x=\frac{12}{6}-\frac{5}{6}$$

Since \frac{12}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}x=\frac{12-5}{6}$$

Subtract 5 from 12 to get 7.

$$\frac{1}{4}x=\frac{7}{6}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x=\frac{7}{6}\times 4$$

Express \frac{7}{6}\times 4 as a single fraction.

$$x=\frac{7\times 4}{6}$$

Multiply 7 and 4 to get 28.

$$x=\frac{28}{6}$$

Reduce the fraction \frac{28}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{14}{3}$$