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If x < y, which of the following must be true?
- a)2x < y
- b)2x > y
- c)x^2 < y^2
- d)2x − y < y
- e)2x − y < 2xy
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If x < y, which of the following must be true?a)2x < yb)2x > ...
If x < y, we can analyze each option to determine which one must be true:
A. 2x < y: We can't determine whether this is true or false since we don't have any information about the relative magnitudes of x and y.
B. 2x > y: We can't determine whether this is true or false since we don't have any information about the relative magnitudes of x and y.
C. x2 < y2: This inequality does not hold true for all values of x and y when x < y. For example, if x = -2 and y = 1, then x2 = 4 and y^2 = 1, which violates the inequality.
D. 2x - y < y: Let's substitute x = 1 and y = 2 to test this inequality. We have 2(1) - 2 < 2, which simplifies to 0 < 2. Since x < y, this inequality is true for the given values of x and y. Since the inequality holds true for at least one case, it must be true.
E. 2x - y < 2xy: We can't determine whether this is true or false since we don't have any information about the relative magnitudes of x and y.
Based on the analysis above, the only option that must be true when x < y is option D.
Therefore, the correct answer is (D).
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If x < y, which of the following must be true?a)2x < yb)2x > ...
If x is a number, then 2x + 3 is an expression representing the sum of twice the number and 3.
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If x < y, which of the following must be true?a)2x < yb)2x > yc)x^2 < y^2d)2x − y < ye)2x − y < 2xyCorrect answer is option 'D'. Can you explain this answer?
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