Explanation:
1. k = 32
k + 19 = 51
32 + 19 = 51
51 = 51
correct, so, k=32 is a valid solution.
2. x = 43
16 = x - 27
16 = 43 - 27
16 = 16
correct, so, x = 43 is a valid solution.
3. m = 9
28 - m = 17
28 - 9 = 17
19 = 17
wrong. so, m = 9 is NOT a valid solution.
4. y = 8
y + 19 = 27
8 + 19 = 27
27 = 27
correct, so, y = 8 is a valid solution.
5. p = 22
19 = p + 3
19 = 22 + 3
19 = 25
wrong. so, p = 22 is NOT a valid solution.
6. r = 11
4 + r = 15
4 + 11 = 15
15 = 15
correct, so, r = 11 is a valid solution.
7.
a - 8 = 9 adding 8 to both sides
a = 17
8.
v + 13 = 15 subtracting 13 from both sides
v = 2
9.
16 = n - 24 adding 24 to both sides
40 = n or n = 40, of course
10.
c - 9 = 16 adding 9 to both sides
c = 25
11.
11 + k = 18 subtracting 11 from both sides
k = 7
12.
15 = w - 7 adding 7 to both sides
22 = w or w = 22, of course