Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.
Expression:
x-y : rational or irrational
3z : rational or irrational
-2x : rational or irrational
y+z : rational or irrational
Expression - Value:
x-y : rational (since the difference between two rational numbers is always rational)
3z : irrational (since the product of a rational number and an irrational number is always irrational)
-2x : rational (since the product of a rational number and a rational number is always rational)
y+z : irrational (since the sum of a rational number and an irrational number is always irrational)