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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Express -\frac{1}{4}\times 2 as a single fraction.

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

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

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

Combine \frac{1}{3}x and -\frac{1}{2}x to get -\frac{1}{6}x.

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

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

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

Since -\frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -8 to get -11.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

Express -\frac{1}{4}\times 2 as a single fraction.

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

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

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

Combine \frac{1}{3}x and -\frac{1}{2}x to get -\frac{1}{6}x.

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

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

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

Since -\frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -8 to get -11.

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