Given statement is "If x < y, then all of the following are true except _____."
so that means we have to find the statement which is not equivalent to x<y.
1. -x < -y
Answer:
divide both side by -1
x > y {inequality sign flips when multiplying or dividing by negative number}
Clearly x<y and x>y are not same.
Hence first choice is wrong.
2. 2x < 2y
Answer:
divide both side by 2
x < y {inequality sign flips only when multiplying or dividing by negative number}
Clearly x<y and x<y are same.
Hence this choice is correct.
3. x + 2 < y + 2
Answer:
subtract 2 from both sides.
x < y {inequality sign flips only when multiplying or dividing by negative number}
Clearly x<y and x<y are same.
Hence this choice is correct.
4. x/2 < y/2
Answer:
multiply both sides by 2.
x < y {inequality sign flips only when multiplying or dividing by negative number}
Clearly x<y and x<y are same.
Hence this choice is correct.