Solve (3(-2)-2(-1))(2(1/2)-24(1/2))+4(-2)^2(-1)^2-(-2)-(-1)/2

$$( 3 ( - 2 ) - 2 ( - 1 ) ) ( 2 ( \frac { 1 } { 2 } ) - 24 ( \frac { 1 } { 2 } ) ) + 4 ( - 2 ) ^ { 2 } ( - 1 ) ^ { 2 } - \frac { ( - 2 ) - ( - 1 ) } { 2 }$$

Evaluate

$$\frac{121}{2}=60.5$$

Solution Steps

Multiply 3 and -2 to get -6.

$$\left(-6-2\left(-1\right)\right)\left(2\times \frac{1}{2}-24\times \frac{1}{2}\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Multiply 2 and -1 to get -2.

$$\left(-6-\left(-2\right)\right)\left(2\times \frac{1}{2}-24\times \frac{1}{2}\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

The opposite of -2 is 2.

$$\left(-6+2\right)\left(2\times \frac{1}{2}-24\times \frac{1}{2}\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Add -6 and 2 to get -4.

$$-4\left(2\times \frac{1}{2}-24\times \frac{1}{2}\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Cancel out 2 and 2.

$$-4\left(1-24\times \frac{1}{2}\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Multiply 24 and \frac{1}{2} to get \frac{24}{2}.

$$-4\left(1-\frac{24}{2}\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Divide 24 by 2 to get 12.

$$-4\left(1-12\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Subtract 12 from 1 to get -11.

$$-4\left(-11\right)+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Multiply -4 and -11 to get 44.

$$44+4\left(-2\right)^{2}\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Calculate -2 to the power of 2 and get 4.

$$44+4\times 4\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Multiply 4 and 4 to get 16.

$$44+16\left(-1\right)^{2}-\frac{-2-\left(-1\right)}{2}$$

Calculate -1 to the power of 2 and get 1.

$$44+16\times 1-\frac{-2-\left(-1\right)}{2}$$

Multiply 16 and 1 to get 16.

$$44+16-\frac{-2-\left(-1\right)}{2}$$

Add 44 and 16 to get 60.

$$60-\frac{-2-\left(-1\right)}{2}$$

The opposite of -1 is 1.

$$60-\frac{-2+1}{2}$$

Add -2 and 1 to get -1.

$$60-\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$60-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$60+\frac{1}{2}$$

Convert 60 to fraction \frac{120}{2}.

$$\frac{120}{2}+\frac{1}{2}$$

Since \frac{120}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{120+1}{2}$$

Add 120 and 1 to get 121.

$$\frac{121}{2}$$

Factor

$$\frac{11 ^ {2}}{2} = 60\frac{1}{2} = 60.5$$