Solve 1/3(2x+1)+1/4(x-2)=

$$\frac { 1 } { 3 } ( 2 x + 1 ) + \frac { 1 } { 4 } ( x - 2 ) =$$

Evaluate

$$\frac{11x}{12}-\frac{1}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 2x+1.

$$\frac{1}{3}\times 2x+\frac{1}{3}+\frac{1}{4}\left(x-2\right)$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{2}{3}x+\frac{1}{3}+\frac{1}{4}\left(x-2\right)$$

Use the distributive property to multiply \frac{1}{4} by x-2.

$$\frac{2}{3}x+\frac{1}{3}+\frac{1}{4}x+\frac{1}{4}\left(-2\right)$$

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

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

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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

Combine \frac{2}{3}x and \frac{1}{4}x to get \frac{11}{12}x.

$$\frac{11}{12}x+\frac{1}{3}-\frac{1}{2}$$

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

$$\frac{11}{12}x+\frac{2}{6}-\frac{3}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{12}x+\frac{2-3}{6}$$

Subtract 3 from 2 to get -1.

$$\frac{11}{12}x-\frac{1}{6}$$

Expand

$$\frac{11x}{12}-\frac{1}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 2x+1.

$$\frac{1}{3}\times 2x+\frac{1}{3}+\frac{1}{4}\left(x-2\right)$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{2}{3}x+\frac{1}{3}+\frac{1}{4}\left(x-2\right)$$

Use the distributive property to multiply \frac{1}{4} by x-2.

$$\frac{2}{3}x+\frac{1}{3}+\frac{1}{4}x+\frac{1}{4}\left(-2\right)$$

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

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

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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

Combine \frac{2}{3}x and \frac{1}{4}x to get \frac{11}{12}x.

$$\frac{11}{12}x+\frac{1}{3}-\frac{1}{2}$$

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

$$\frac{11}{12}x+\frac{2}{6}-\frac{3}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{12}x+\frac{2-3}{6}$$

Subtract 3 from 2 to get -1.

$$\frac{11}{12}x-\frac{1}{6}$$