Quantity A = y - x > 12 - 5 = 7 = B
--> A > B
--> A
Note: x < 5 --> -x > -5

why cant X be negative?

Of course, x can be negative. And when x is negative, y - x will always be larger than y. You can pick specific number to see what happens.(12 - -1) > 12
Hope it helps.

P/s: You should know the principle as follows

A > B (A - B > 0)
C > D (C - D > 0)
--> plus 2 inequalities, we have
A - D > B - C

Posted from my mobile device

Can you please give me the list of inequality principle?

Use this book.

Regards

very useful book, I have just gone through a few sections,
easy to understand, many concepts are more clear now.
Thanx, stay blessed.

let B is your benchmark.
think of the max. value for x, let say it will be 4.9999
think of the minimum value for y, let say is 12.0001

then subtract : 12.0001-4.9999= 7.0002
still A greater

Useful property: If the inequality symbols of two inequalities are facing the same direction, we can add those inequalities.
For example, if \(w > x\) and \(y > z\), then it must also be true that \(w+y > x+z\)

Given:
\(y > 12\)
\(x < 5\)

At this point, the inequality symbols are not facing the same direction.
However, we can multiply both sides of the bottom inequality by \(-1\) to get:
\(y > 12\)
\(-x > -5\) [Since we multiplied both sides of the inequality by a negative value, we had to reverse the direction of the inequality symbol (see video below for more on this) ]

Now that the inequality symbols are facing the same direction, we can add the two inequalities to get: \(y + (-x)> 12 + (-5)\), which simplifies to be: \(y - x > 7\), Which means quantity A is greater.

Answer: A

Aside: An alternative approach is to use some number sense and recognize that, if we subtract a number smaller than 5 from a number that is greater than 12, the result must be greater than 7.


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