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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Combine 3x and \frac{1}{6}x to get \frac{19}{6}x.

$$\frac{19}{6}x-\frac{2}{3}=\frac{5}{2}$$

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

$$\frac{19}{6}x=\frac{5}{2}+\frac{2}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{19}{6}x=\frac{15}{6}+\frac{4}{6}$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{19}{6}x=\frac{15+4}{6}$$

Add 15 and 4 to get 19.

$$\frac{19}{6}x=\frac{19}{6}$$

Multiply both sides by \frac{6}{19}, the reciprocal of \frac{19}{6}.

$$x=\frac{19}{6}\times \frac{6}{19}$$

Cancel out \frac{19}{6} and its reciprocal \frac{6}{19}.

$$x=1$$