Why does changing a subrtraction problem to an addition with the complement of 9 work

Step-by-step explanation:

When we need to subtract a number from another number, in that case, we can take the complement of the first number to add it to the second number, the result will be the same. It is because when we take the complement of 9 of that number, it will represent the negative of that number. Hence, by adding the negative of a number we will get the same result as we get after subtraction.

For example:

Subtract 213 from 843

843 - 213 = 630

complement of 9 of 213= 999-213

                                       =786

Now, add 786 and 843

786+843=1629

We got the result in 4 digits so by adding the left-most digit to the right-sided three-digit number of the result, we will get

629+1 = 630

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal