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

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

Evaluate

$$\frac{x-22}{12}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 3x-2.

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

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

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

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

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

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

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

Use the distributive property to multiply -\frac{1}{3} by 2x+4.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Express -\frac{1}{3}\times 4 as a single fraction.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

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

$$\frac{1}{12}x-\frac{1}{2}-\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{1}{12}x-\frac{3}{6}-\frac{8}{6}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}x+\frac{-3-8}{6}$$

Subtract 8 from -3 to get -11.

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

Expand

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

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 3x-2.

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

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

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

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

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

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

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

Use the distributive property to multiply -\frac{1}{3} by 2x+4.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Express -\frac{1}{3}\times 4 as a single fraction.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

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

$$\frac{1}{12}x-\frac{1}{2}-\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{1}{12}x-\frac{3}{6}-\frac{8}{6}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}x+\frac{-3-8}{6}$$

Subtract 8 from -3 to get -11.

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