Q5. A taxi charges ₹50 plus ₹12 per km. Write an inequality for the distance d km that keeps the fare within ₹290, and find the greatest distance.
50 + 12d ≤ 290, so 12d ≤ 240 and d ≤ 20: at most 20 km.
Q6. Is 5 < 5 true? Is 5 ≤ 5 true? What does this show about strict and slack inequalities?
5 < 5 is false and 5 ≤ 5 is true: a slack inequality allows the two sides to be equal, a strict one does not.
Q7. For Reshma (40x + 20y ≤ 120, whole numbers x, y ≥ 0), how many choices spend exactly ₹120, and which are they?
40x + 20y = 120; dividing by 20, 2x + y = 6: (0, 6), (1, 4), (2, 2) and (3, 0), so 4 choices.
Q8. Write a double inequality for “the temperature T stayed between 30 °C and 35 °C, both included”, and give it as an interval.
30 ≤ T ≤ 35, the closed interval [30, 35].