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

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

Evaluate

$$b-6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$4\left(b-3\right)-2\left(\frac{3b}{2}-\frac{3\times 2}{2}\right)$$

Since \frac{3b}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$4\left(b-3\right)-2\times \frac{3b-3\times 2}{2}$$

Do the multiplications in 3b-3\times 2.

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

Cancel out 2 and 2.

$$4\left(b-3\right)-\left(3b-6\right)$$

Use the distributive property to multiply 4 by b-3.

$$4b-12-\left(3b-6\right)$$

To find the opposite of 3b-6, find the opposite of each term.

$$4b-12-3b-\left(-6\right)$$

The opposite of -6 is 6.

$$4b-12-3b+6$$

Combine 4b and -3b to get b.

$$b-12+6$$

Add -12 and 6 to get -6.

$$b-6$$

Expand

$$b-6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$4\left(b-3\right)-2\left(\frac{3b}{2}-\frac{3\times 2}{2}\right)$$

Since \frac{3b}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$4\left(b-3\right)-2\times \frac{3b-3\times 2}{2}$$

Do the multiplications in 3b-3\times 2.

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

Cancel out 2 and 2.

$$4\left(b-3\right)-\left(3b-6\right)$$

Use the distributive property to multiply 4 by b-3.

$$4b-12-\left(3b-6\right)$$

To find the opposite of 3b-6, find the opposite of each term.

$$4b-12-3b-\left(-6\right)$$

The opposite of -6 is 6.

$$4b-12-3b+6$$

Combine 4b and -3b to get b.

$$b-12+6$$

Add -12 and 6 to get -6.

$$b-6$$