Mathematics
If a > b and m < 0, then which of the following is correct :
- am < bm
- am = bm
- am > bm
- am and bm cannot be compared
Linear Inequations
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Answer
Given:
a > b
m < 0 means m is negative.
Let's evaluate each:
- am < bm
Multiplying an inequality by a negative number (m < 0) requires reversing the inequality sign. It is correct.
- am = bm
Multiplying by a non-zero number (m < 0) maintains a difference between unequal values; they cannot become equal. It is incorrect.
- am > bm
This is incorrect because, m is negative number and multiplying an inequality by a negative number requires reversing the inequality sign. But here the sign remains same.
- am and bm cannot be compared
Since the relationship between a, b and the sign of m is known, their products are strictly comparable. It is incorrect.
Among all four options, option 1 is correct.
Hence, option 1 is the correct option.
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