Solve 13/6+3/2x=x+7/3

$$\frac { 13 } { 6 } + \frac { 3 } { 2 } x = x + \frac { 7 } { 3 }$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$\frac{13}{6}+\frac{3}{2}x-x=\frac{7}{3}$$

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

$$\frac{13}{6}+\frac{1}{2}x=\frac{7}{3}$$

Subtract \frac{13}{6} from both sides.

$$\frac{1}{2}x=\frac{7}{3}-\frac{13}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{13}{6} to fractions with denominator 6.

$$\frac{1}{2}x=\frac{14}{6}-\frac{13}{6}$$

Since \frac{14}{6} and \frac{13}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{14-13}{6}$$

Subtract 13 from 14 to get 1.

$$\frac{1}{2}x=\frac{1}{6}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{1}{6}\times 2$$

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

$$x=\frac{2}{6}$$

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

$$x=\frac{1}{3}$$