Why is first equation is x negative and in equations 2,3 & 4 answers are not negative and also sign changes?

1)Equation: x+y>1

Answer: y=-x+1

2)Equation: x-y>5

Answer: y<x-5

3)Equation: 3x-y<2

Answer: y>3x-2

Sign is greater than or equal to in the following equation.

4)Equation: x-3y>9

Sign is less than or equal to in the answer.

Answer: y<1/3x-3

In equation 1, the > cannot chamge to =

Subtract x from both sides to get
y > -x+1

In equation 2, add y-5 to both sides to get x-5 > y, thish is the same as
y < x-5