Solve {l}{-21:(-3)+(-12):(+6)-(-1)(-6)-(-40):8-(+4):(-2)}{(-2)[13+(-8)-(-7)]:(+3)-[(2-23):(-7)](-2)}

$$\left. \begin{array} { l } { - 21 : ( - 3 ) + ( - 12 ) : ( + 6 ) - ( - 1 ) ( - 6 ) - ( - 40 ) : 8 - ( + 4 ) : ( - 2 ) } \\ { ( - 2 ) [ 13 + ( - 8 ) - ( - 7 ) ] : ( + 3 ) - [ ( 2 - 23 ) : ( - 7 ) ] ( - 2 ) } \end{array} \right.$$

Sort

$$-2,6$$

Solution Steps

Divide -21 by -3 to get 7.

$$sort(7+\frac{-12}{6}-\left(-\left(-6\right)\right)-\frac{-40}{8}-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Divide -12 by 6 to get -2.

$$sort(7-2-\left(-\left(-6\right)\right)-\frac{-40}{8}-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Subtract 2 from 7 to get 5.

$$sort(5-\left(-\left(-6\right)\right)-\frac{-40}{8}-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Multiply -1 and -6 to get 6.

$$sort(5-6-\frac{-40}{8}-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Subtract 6 from 5 to get -1.

$$sort(-1-\frac{-40}{8}-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Divide -40 by 8 to get -5.

$$sort(-1-\left(-5\right)-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

The opposite of -5 is 5.

$$sort(-1+5-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Add -1 and 5 to get 4.

$$sort(4-\frac{4}{-2},\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Divide 4 by -2 to get -2.

$$sort(4-\left(-2\right),\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

The opposite of -2 is 2.

$$sort(4+2,\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Add 4 and 2 to get 6.

$$sort(6,\frac{-2\left(13-8-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Subtract 8 from 13 to get 5.

$$sort(6,\frac{-2\left(5-\left(-7\right)\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

The opposite of -7 is 7.

$$sort(6,\frac{-2\left(5+7\right)}{3}-\frac{2-23}{-7}\left(-2\right))$$

Add 5 and 7 to get 12.

$$sort(6,\frac{-2\times 12}{3}-\frac{2-23}{-7}\left(-2\right))$$

Multiply -2 and 12 to get -24.

$$sort(6,\frac{-24}{3}-\frac{2-23}{-7}\left(-2\right))$$

Divide -24 by 3 to get -8.

$$sort(6,-8-\frac{2-23}{-7}\left(-2\right))$$

Subtract 23 from 2 to get -21.

$$sort(6,-8-\frac{-21}{-7}\left(-2\right))$$

Divide -21 by -7 to get 3.

$$sort(6,-8-3\left(-2\right))$$

Multiply 3 and -2 to get -6.

$$sort(6,-8-\left(-6\right))$$

The opposite of -6 is 6.

$$sort(6,-8+6)$$

Add -8 and 6 to get -2.

$$sort(6,-2)$$

To sort the list, start from a single element 6.

$$6$$

Insert -2 to the appropriate location in the new list.

$$-2,6$$

Evaluate

$$6,\ -2$$