-9c-12+3c=12
-9c+3c=+12+12
-6=+24
c= - 4
Prove that if m + n and n + p are even integers, where m, n, and p are integers, then m + p is even.
m=2k-n, p=2l-n
Let m+n and n+p be even integers, thus m+n=2k and n+p=2l by definition of even
m+p= 2k-n + 2l-n substitution
= 2k+2l-2n
=2 (k+l-n)
=2x, where x=k+l-n ∈Z (integers)
Hence, m+p is even by direct proof.
31 is the answer; this is because to get to the place-holder number “0” you have to add 19 to -19, then after this, you add 12, making the total 31.
