Let a be a rational number and x be an irrational number.

Let a be a rational number and x be an irrational number.

Counter evidence
Suppose a+x is a rational number
X=(a+x)-a=rational-rational=rational
Rational number 1= m1/n1
Rational number 2= m2/n2
M1,m2,n1,n2 are all integers.
M1/n1-m2/n2=(m1n2-n1m2)/(n1n2) is a rational number
Contradiction with x being irrational
So a+x is an irrational number.

If ab is not equal to 0, try to write the absolute value of a + b + c. Come on! To process, and, tell me why. If ab is not equal to 0, try to write out all possible values of absolute value of a + b + b. If ab is not equal to 0, try to write the absolute value of a + b + c. Come on! To the process, and, tell me why. If ab is not equal to 0, try to write out all possible values of absolute value of a + b + b.

If ab=0, the absolute value of a part of a + the absolute value of b part of b
Number of 1>2 is greater than 0
Absolute value of a part + absolute value of b part =2
The number of "2" and "1" is greater than 0, and the number is less than 0.
Absolute value of a part + absolute value of b part =0
3"2 Is less than 0
Absolute value of a part + absolute value of b part =-2

If ab=0, the absolute value of a part a + the absolute value of b part b
Number of 1>2 is greater than 0
Absolute value of a part + absolute value of b part =2
The number of "2" and "1" is greater than 0, and the number is less than 0.
Absolute value of a part + absolute value of b part =0
3"2 Is less than 0
Absolute value of a part + absolute value of b part =-2