Solve 3x-2/3+2/3x-1/2

$$3 x - \frac { 2 } { 3 } + \frac { 2 } { 3 } x - \frac { 1 } { 2 }$$

Evaluate

$$\frac{11x}{3}-\frac{7}{6}$$

Solution Steps

Combine 3x and \frac{2}{3}x to get \frac{11}{3}x.

$$\frac{11}{3}x-\frac{2}{3}-\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{11}{3}x-\frac{4}{6}-\frac{3}{6}$$

Since -\frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{3}x+\frac{-4-3}{6}$$

Subtract 3 from -4 to get -7.

$$\frac{11}{3}x-\frac{7}{6}$$

Factor

$$\frac{22x-7}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{22x-7}{6}$$

Consider 18x-4+4x-3. Multiply and combine like terms.

$$22x-7$$

Rewrite the complete factored expression.

$$\frac{22x-7}{6}$$