give a direct proof for each of the following statements about the integers.

if x is even and y is odd, then x + y is odd.

See explanation below

Step-by-step explanation:

If x is even, then we know that x = 2k for a k ≥1

If y is odd, then we know that y = 2j -1 for a j≥1

Therefore, x + y can be written similarly as:

And clearly, 2(k + j) -1 is odd.

Therefore, the sum x + y is an odd number.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a