Solve {l}{-(-5)+(-6)}{-18+4-(-9)}{14+(-16)-(+15)-(-21)}{26-(-24)+(-90)-(-32)+(-75)}{(9-17)[phone]}{-(4-17)-10-7+(-16)-(-20)}{7-8-(-12+21)+(-16)-(-23)}

$$\left. \begin{array} { l } { - ( - 5 ) + ( - 6 ) } \\ { - 18 + 4 - ( - 9 ) } \\ { 14 + ( - 16 ) - ( + 15 ) - ( - 21 ) } \\ { 26 - ( - 24 ) + ( - 90 ) - ( - 32 ) + ( - 75 ) } \\ { ( 9 - 17 ) + 11 - ( 55 - 78 ) - 18 } \\ { - ( 4 - 17 ) - 10 - 7 + ( - 16 ) - ( - 20 ) } \\ { 7 - 8 - ( - 12 + 21 ) + ( - 16 ) - ( - 23 ) } \end{array} \right.$$

Sort

$$-83,-5,-3,-1,0,4,8$$

Solution Steps

The opposite of -5 is 5.

$$sort(5-6,-18+4-\left(-9\right),14-16-15-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 6 from 5 to get -1.

$$sort(-1,-18+4-\left(-9\right),14-16-15-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add -18 and 4 to get -14.

$$sort(-1,-14-\left(-9\right),14-16-15-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -9 is 9.

$$sort(-1,-14+9,14-16-15-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add -14 and 9 to get -5.

$$sort(-1,-5,14-16-15-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 16 from 14 to get -2.

$$sort(-1,-5,-2-15-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 15 from -2 to get -17.

$$sort(-1,-5,-17-\left(-21\right),26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -21 is 21.

$$sort(-1,-5,-17+21,26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add -17 and 21 to get 4.

$$sort(-1,-5,4,26-\left(-24\right)-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -24 is 24.

$$sort(-1,-5,4,26+24-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add 26 and 24 to get 50.

$$sort(-1,-5,4,50-90-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 90 from 50 to get -40.

$$sort(-1,-5,4,-40-\left(-32\right)-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -32 is 32.

$$sort(-1,-5,4,-40+32-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add -40 and 32 to get -8.

$$sort(-1,-5,4,-8-75,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 75 from -8 to get -83.

$$sort(-1,-5,4,-83,9-17+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 17 from 9 to get -8.

$$sort(-1,-5,4,-83,-8+11-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add -8 and 11 to get 3.

$$sort(-1,-5,4,-83,3-\left(55-78\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 78 from 55 to get -23.

$$sort(-1,-5,4,-83,3-\left(-23\right)-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -23 is 23.

$$sort(-1,-5,4,-83,3+23-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add 3 and 23 to get 26.

$$sort(-1,-5,4,-83,26-18,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 18 from 26 to get 8.

$$sort(-1,-5,4,-83,8,-\left(4-17\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 17 from 4 to get -13.

$$sort(-1,-5,4,-83,8,-\left(-13\right)-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -13 is 13.

$$sort(-1,-5,4,-83,8,13-10-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 10 from 13 to get 3.

$$sort(-1,-5,4,-83,8,3-7-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 7 from 3 to get -4.

$$sort(-1,-5,4,-83,8,-4-16-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 16 from -4 to get -20.

$$sort(-1,-5,4,-83,8,-20-\left(-20\right),7-8-\left(-12+21\right)-16-\left(-23\right))$$

The opposite of -20 is 20.

$$sort(-1,-5,4,-83,8,-20+20,7-8-\left(-12+21\right)-16-\left(-23\right))$$

Add -20 and 20 to get 0.

$$sort(-1,-5,4,-83,8,0,7-8-\left(-12+21\right)-16-\left(-23\right))$$

Subtract 8 from 7 to get -1.

$$sort(-1,-5,4,-83,8,0,-1-\left(-12+21\right)-16-\left(-23\right))$$

Add -12 and 21 to get 9.

$$sort(-1,-5,4,-83,8,0,-1-9-16-\left(-23\right))$$

Subtract 9 from -1 to get -10.

$$sort(-1,-5,4,-83,8,0,-10-16-\left(-23\right))$$

Subtract 16 from -10 to get -26.

$$sort(-1,-5,4,-83,8,0,-26-\left(-23\right))$$

The opposite of -23 is 23.

$$sort(-1,-5,4,-83,8,0,-26+23)$$

Add -26 and 23 to get -3.

$$sort(-1,-5,4,-83,8,0,-3)$$

To sort the list, start from a single element -1.

$$-1$$

Insert -5 to the appropriate location in the new list.

$$-5,-1$$

Insert 4 to the appropriate location in the new list.

$$-5,-1,4$$

Insert -83 to the appropriate location in the new list.

$$-83,-5,-1,4$$

Insert 8 to the appropriate location in the new list.

$$-83,-5,-1,4,8$$

Insert 0 to the appropriate location in the new list.

$$-83,-5,-1,0,4,8$$

Insert -3 to the appropriate location in the new list.

$$-83,-5,-3,-1,0,4,8$$

Evaluate

$$-1,\ -5,\ 4,\ -83,\ 8,\ 0,\ -3$$