Solve 1/4(3x-1)+1/6(x+3)=

$$\frac { 1 } { 4 } ( 3 x - 1 ) + \frac { 1 } { 6 } ( x + 3 ) =$$

Evaluate

$$\frac{11x}{12}+\frac{1}{4}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 3x-1.

$$\frac{1}{4}\times 3x+\frac{1}{4}\left(-1\right)+\frac{1}{6}\left(x+3\right)$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{3}{4}x+\frac{1}{4}\left(-1\right)+\frac{1}{6}\left(x+3\right)$$

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

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}\left(x+3\right)$$

Use the distributive property to multiply \frac{1}{6} by x+3.

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}x+\frac{1}{6}\times 3$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}x+\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}x+\frac{1}{2}$$

Combine \frac{3}{4}x and \frac{1}{6}x to get \frac{11}{12}x.

$$\frac{11}{12}x-\frac{1}{4}+\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{11}{12}x-\frac{1}{4}+\frac{2}{4}$$

Since -\frac{1}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{11}{12}x+\frac{-1+2}{4}$$

Add -1 and 2 to get 1.

$$\frac{11}{12}x+\frac{1}{4}$$

Expand

$$\frac{11x}{12}+\frac{1}{4}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 3x-1.

$$\frac{1}{4}\times 3x+\frac{1}{4}\left(-1\right)+\frac{1}{6}\left(x+3\right)$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{3}{4}x+\frac{1}{4}\left(-1\right)+\frac{1}{6}\left(x+3\right)$$

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

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}\left(x+3\right)$$

Use the distributive property to multiply \frac{1}{6} by x+3.

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}x+\frac{1}{6}\times 3$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}x+\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}x-\frac{1}{4}+\frac{1}{6}x+\frac{1}{2}$$

Combine \frac{3}{4}x and \frac{1}{6}x to get \frac{11}{12}x.

$$\frac{11}{12}x-\frac{1}{4}+\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{11}{12}x-\frac{1}{4}+\frac{2}{4}$$

Since -\frac{1}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{11}{12}x+\frac{-1+2}{4}$$

Add -1 and 2 to get 1.

$$\frac{11}{12}x+\frac{1}{4}$$