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\(x < 5\) and \(y > 12\)
Quantity A
Quantity B
\(y-x\)
\(7\)
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Re: x < 5 and y > 12
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24 Sep 2018, 20:09
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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
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
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.