Solve 1/3(x-2)-1/4(x-5)=

$$\frac { 1 } { 3 } ( x - 2 ) - \frac { 1 } { 4 } ( x - 5 ) =$$

Evaluate

$$\frac{x+7}{12}$$

Solution Steps

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

$$\frac{1}{3}x+\frac{1}{3}\left(-2\right)-\frac{1}{4}\left(x-5\right)$$

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

$$\frac{1}{3}x+\frac{-2}{3}-\frac{1}{4}\left(x-5\right)$$

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

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}\left(x-5\right)$$

Use the distributive property to multiply -\frac{1}{4} by x-5.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}x-\frac{1}{4}\left(-5\right)$$

Express -\frac{1}{4}\left(-5\right) as a single fraction.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}x+\frac{-\left(-5\right)}{4}$$

Multiply -1 and -5 to get 5.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}x+\frac{5}{4}$$

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

$$\frac{1}{12}x-\frac{2}{3}+\frac{5}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{1}{12}x-\frac{8}{12}+\frac{15}{12}$$

Since -\frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}x+\frac{-8+15}{12}$$

Add -8 and 15 to get 7.

$$\frac{1}{12}x+\frac{7}{12}$$

Expand

$$\frac{x+7}{12}$$

Solution Steps

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

$$\frac{1}{3}x+\frac{1}{3}\left(-2\right)-\frac{1}{4}\left(x-5\right)$$

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

$$\frac{1}{3}x+\frac{-2}{3}-\frac{1}{4}\left(x-5\right)$$

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

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}\left(x-5\right)$$

Use the distributive property to multiply -\frac{1}{4} by x-5.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}x-\frac{1}{4}\left(-5\right)$$

Express -\frac{1}{4}\left(-5\right) as a single fraction.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}x+\frac{-\left(-5\right)}{4}$$

Multiply -1 and -5 to get 5.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{4}x+\frac{5}{4}$$

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

$$\frac{1}{12}x-\frac{2}{3}+\frac{5}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{1}{12}x-\frac{8}{12}+\frac{15}{12}$$

Since -\frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}x+\frac{-8+15}{12}$$

Add -8 and 15 to get 7.

$$\frac{1}{12}x+\frac{7}{12}$$