Solve 2/3[4a-3b)+1/3b-1/4(6a+7b)]

$$\frac { 2 } { 3 } [ 4 a - 3 b ) + \frac { 1 } { 3 } b - \frac { 1 } { 4 } ( 6 a + 7 b ) ]$$

Evaluate

$$\frac{7a}{6}-\frac{41b}{12}$$

Solution Steps

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

$$\frac{2}{3}\times 4a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Express \frac{2}{3}\times 4 as a single fraction.

$$\frac{2\times 4}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Express \frac{2}{3}\left(-3\right) as a single fraction.

$$\frac{8}{3}a+\frac{2\left(-3\right)}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Multiply 2 and -3 to get -6.

$$\frac{8}{3}a+\frac{-6}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Divide -6 by 3 to get -2.

$$\frac{8}{3}a-2b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Combine -2b and \frac{1}{3}b to get -\frac{5}{3}b.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Use the distributive property to multiply -\frac{1}{4} by 6a+7b.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\times 6a-\frac{1}{4}\times 7b$$

Express -\frac{1}{4}\times 6 as a single fraction.

$$\frac{8}{3}a-\frac{5}{3}b+\frac{-6}{4}a-\frac{1}{4}\times 7b$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{1}{4}\times 7b$$

Express -\frac{1}{4}\times 7 as a single fraction.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a+\frac{-7}{4}b$$

Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{7}{4}b$$

Combine \frac{8}{3}a and -\frac{3}{2}a to get \frac{7}{6}a.

$$\frac{7}{6}a-\frac{5}{3}b-\frac{7}{4}b$$

Combine -\frac{5}{3}b and -\frac{7}{4}b to get -\frac{41}{12}b.

$$\frac{7}{6}a-\frac{41}{12}b$$

Expand

$$\frac{7a}{6}-\frac{41b}{12}$$

Solution Steps

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

$$\frac{2}{3}\times 4a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Express \frac{2}{3}\times 4 as a single fraction.

$$\frac{2\times 4}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Express \frac{2}{3}\left(-3\right) as a single fraction.

$$\frac{8}{3}a+\frac{2\left(-3\right)}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Multiply 2 and -3 to get -6.

$$\frac{8}{3}a+\frac{-6}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Divide -6 by 3 to get -2.

$$\frac{8}{3}a-2b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Combine -2b and \frac{1}{3}b to get -\frac{5}{3}b.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\left(6a+7b\right)$$

Use the distributive property to multiply -\frac{1}{4} by 6a+7b.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\times 6a-\frac{1}{4}\times 7b$$

Express -\frac{1}{4}\times 6 as a single fraction.

$$\frac{8}{3}a-\frac{5}{3}b+\frac{-6}{4}a-\frac{1}{4}\times 7b$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{1}{4}\times 7b$$

Express -\frac{1}{4}\times 7 as a single fraction.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a+\frac{-7}{4}b$$

Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{7}{4}b$$

Combine \frac{8}{3}a and -\frac{3}{2}a to get \frac{7}{6}a.

$$\frac{7}{6}a-\frac{5}{3}b-\frac{7}{4}b$$

Combine -\frac{5}{3}b and -\frac{7}{4}b to get -\frac{41}{12}b.

$$\frac{7}{6}a-\frac{41}{12}b$$