Solve 3/4[2(4a-b)-5(a-2b)]

$$\frac { 3 } { 4 } [ 2 ( 4 a - b ) - 5 ( a - 2 b ) ]$$

Evaluate

$$\frac{9a}{4}+6b$$

Solution Steps

Use the distributive property to multiply 2 by 4a-b.

$$\frac{3}{4}\left(8a-2b-5\left(a-2b\right)\right)$$

Use the distributive property to multiply -5 by a-2b.

$$\frac{3}{4}\left(8a-2b-5a+10b\right)$$

Combine 8a and -5a to get 3a.

$$\frac{3}{4}\left(3a-2b+10b\right)$$

Combine -2b and 10b to get 8b.

$$\frac{3}{4}\left(3a+8b\right)$$

Use the distributive property to multiply \frac{3}{4} by 3a+8b.

$$\frac{3}{4}\times 3a+\frac{3}{4}\times 8b$$

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

$$\frac{3\times 3}{4}a+\frac{3}{4}\times 8b$$

Multiply 3 and 3 to get 9.

$$\frac{9}{4}a+\frac{3}{4}\times 8b$$

Express \frac{3}{4}\times 8 as a single fraction.

$$\frac{9}{4}a+\frac{3\times 8}{4}b$$

Multiply 3 and 8 to get 24.

$$\frac{9}{4}a+\frac{24}{4}b$$

Divide 24 by 4 to get 6.

$$\frac{9}{4}a+6b$$

Expand

$$\frac{9a}{4}+6b$$

Solution Steps

Use the distributive property to multiply 2 by 4a-b.

$$\frac{3}{4}\left(8a-2b-5\left(a-2b\right)\right)$$

Use the distributive property to multiply -5 by a-2b.

$$\frac{3}{4}\left(8a-2b-5a+10b\right)$$

Combine 8a and -5a to get 3a.

$$\frac{3}{4}\left(3a-2b+10b\right)$$

Combine -2b and 10b to get 8b.

$$\frac{3}{4}\left(3a+8b\right)$$

Use the distributive property to multiply \frac{3}{4} by 3a+8b.

$$\frac{3}{4}\times 3a+\frac{3}{4}\times 8b$$

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

$$\frac{3\times 3}{4}a+\frac{3}{4}\times 8b$$

Multiply 3 and 3 to get 9.

$$\frac{9}{4}a+\frac{3}{4}\times 8b$$

Express \frac{3}{4}\times 8 as a single fraction.

$$\frac{9}{4}a+\frac{3\times 8}{4}b$$

Multiply 3 and 8 to get 24.

$$\frac{9}{4}a+\frac{24}{4}b$$

Divide 24 by 4 to get 6.

$$\frac{9}{4}a+6b$$