Mathematics
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 < .
Linear Inequations
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Answer
(i) True
Reason — Any mathematical statement that uses inequality symbols like <, >, ≤, or ≥ to compare two expressions is defined as an inequation.
(ii) True
Reason — This follows the Negative Division Rule. When we divide both sides of an inequality by a negative number (m < 0), the direction of the inequality sign must be reversed (< becomes >).
(iii) False
Reason — Adding or subtracting any number (whether positive or negative) from both sides of an inequality never changes the direction of the sign.
If a < b, then a - m < b - m remains true regardless of the value of m.
(iv) True
Reason — Similar to the division rule, multiplying by a negative number (m < 0) requires flipping the sign.
(v) False
Reason — When we divide by a positive number (m > 0), the inequality sign stays the same. Therefore, if a > b, the result should be .
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Related Questions
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 ⇒ < .
Fill in the blanks :
(i) A statement of inequality between two expressions is called an …………… .
(ii) The set from which the values of the variable satisfying a given inequality are chosen, is called the …………… .
(iii) Subset of the replacement set, consisting of all those values of the variable which satisfy the given inequation is called the …………… .
(iv) Multiplying each side of an inequality by a negative number, …………… the inequality.
(v) If a ≠ 0, b ≠ 0 and a < b, then …………… .
Madan Singh runs a rental car company. He charges ₹ 250 per day plus ₹ 15 for every kilometre the car is driven. Professor Dayal rents a car for 1 day, while his own car is being repaired. He assures Madan Singh that he will pay him more than ₹ 500 as rent for the day.
(1) The inequality for the rent paid by Dayal for 1 day is :
- 3x < 100
- x > 25
- 3x > 50
- x < 75
(2) The solution set for the inequality obtained above is given by :
- {16, 17, 18, ……………}
- {17, 18, 19, ……………}
- {19, 20, 21, ……………}
- {20, 21, 22, ……………}
(3) Dayal estimated that the rent for 1 day would be less than ₹ 600 as he calculated the distance he has to drive the car. The inequality for the rent in this case would be :
- y > 30
- 2y < 35
- 3y < 70
- 4y > 45
(4) The solution set for the above inequality is given by :
- {……………, 20, 21, 22, 23}
- {……………, 17, 18, 19, 20}
- {……………, 18, 19, 20, 21}
- {……………, 15, 16, 17, 18}
Assertion: If 2x + 3 > 8, then 2x + 3 - 3 > 8 - 3.
Reason: Subtracting a number from each side of an inequality reverses the inequality.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.