Question

If x < y, then all of the following are true except _____.

1. -x < -y
2. 2x < 2y
3. x + 2 < y + 2
4. x/2 < y/2

Answer 1

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.

Answer 2

1. - x < -y

Step by step explanation

When we multiply, add and divide the value remains the same.

But when you change the sign, the inequality direction will be > in this case, otherwise that is not ture.

For instance,

2 < 3

-2 < -3 is not true.

Because -2 is greater than -3

Hope this will help you.

Thank you. :)