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 $\dfrac{1}{a}$ …………… $\dfrac{1}{b}$.

Write true (T) or false (F) :

(i) $\dfrac{2}{3}x - \dfrac{4}{5}$ ≥ 8 is an inequation.

(ii) If a < b and m < 0, then $\dfrac{a}{m}$ > $\dfrac{b}{m}$.

(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 $\dfrac{a}{m}$ < $\dfrac{b}{m}$.

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 :

1. 3x < 100
2. x > 25
3. 3x > 50
4. x < 75

(2) The solution set for the inequality obtained above is given by :

1. {16, 17, 18, ……………}
2. {17, 18, 19, ……………}
3. {19, 20, 21, ……………}
4. {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 :

1. y > 30
2. 2y < 35
3. 3y < 70
4. 4y > 45

(4) The solution set for the above inequality is given by :

1. {……………, 20, 21, 22, 23}
2. {……………, 17, 18, 19, 20}
3. {……………, 18, 19, 20, 21}
4. {……………, 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.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.