1) Adding an irrational number and a rational number will always give you an irrational number.
2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
The set of rational numbers is closed under the basic operations of arithmetic.
Suppose 3 + 2x5 is rational.
Subtract 3, which is a rational number: then 2x5 is rational
Divide by 2, a rational number: then x5 is rational.
But you are given that x5 is irrational therefore the supposition was wrong. That is, 3 + 2x5 is not rational.
This can't be proved because it is not necessarily true. If x is 2 and y is 1 then x-y is 1, which is rational. The product of 2x and 3y is 12, which is also rational. Sadly, you can't disprove it either; for certain values of x,y it is true as posited.
2x + 27, where x is your number
2X+20 Where "X" is your number.
(Y = -2x plus or minus any number) is parallel to (Y = -2x + 5) .
2x+4y
This can't be proved because it is not necessarily true. If x is 2 and y is 1 then x-y is 1, which is rational. The product of 2x and 3y is 12, which is also rational. Sadly, you can't disprove it either; for certain values of x,y it is true as posited.
2x + 27, where x is your number
[ y = 2x plus or minus any number ] is parallel to it. [ y = -0.5x plus or minus any number ] is perpendicular to it.
2X+20 Where "X" is your number.
2x + 27
8x-4
[ y = -2x + any other number ] is parallel to [ y = -2x + 6 ].
(Y = -2x plus or minus any number) is parallel to (Y = -2x + 5) .
2x+4y
3x + 2x - 8x + 2x = -x
x=1
eigthy one plus a number