Mathematics
Which one of the following statements is incorrect?
If a < b, then a - m < b - m
If a > b and m > 0, then am > bm
If a < b and m > 0, then > .
If a ≠ 0 and b ≠ 0, then a > b ⇒ < .
Linear Inequations
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Answer
Let's evaluate each:
If a < b, then a - m < b - m
Adding/Subtracting doesn't change the sign. So, it is correct.If a > b and m > 0, then am > bm
Multiplying by a positive number keeps the sign. So, it is correct.If a < b and m > 0, then > .
Incorrect. If we divide by a positive number, the sign should remain the same. It should be < .If a ≠ 0 and b ≠ 0, then a > b ⇒ < .
Generally correct for positive numbers (Reciprocal rule).
Option 3 is the incorrect statement.
Hence, option 3 is the correct option.
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Fill in the blanks :
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(iii) Subset of the replacement set, consisting of all those values of the variable which satisfy the given inequation is called the …………… .
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Write true (T) or false (F) :
(i) ≥ 8 is an inequation.
(ii) If a < b and m < 0, then > .
(iii) If a < b, m < 0, then a - m > b - m.
(iv) If a > b and m < 0, then am < bm.
(v) If a > b and m > 0, then < .