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Lecture - 4 Chapter 6 Linear Inequalities

NCERT Miscellaneous Exercise

Solve the inequalities in Exercises 1 to 6.

Question 1. $2 \leq 3x - 4 \leq 5$

Question 2. $6 \leq - 3 (2x - 4) < 12$

Question 3. $-3 \le 4 – \frac{7x}{2} \le 18$

Question 4. $-15 < \frac{3(x-2)}{5} \le 0$

Question 5. $-12 < 4 – \frac{3x}{-5} \le 2$

Question 6. $7 \le \frac{(3x+11)}{2} \le 11$

Solve the inequalities in Exercises 7 to 10 and represent the solution graphically on number line.

Question 7. $5x + 1 > - 24, 5x - 1 < 24$

Question 8. $2 (x - 1) < x + 5, 3 (x + 2) > 2 - x$

Question 9. $3x - 7 > 2 (x - 6) , 6 - x > 11 - 2x$

Question 10. $5 (2x - 7) - 3 (2x + 3) \leq 0 , 2x + 19 \leq 6x + 47$

Question 11. A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by $F = \frac{9}{5} C + 32$

Question 12. A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Question 13. How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Question 14. IQ of a person is given by the formula $IQ = \frac{MA}{CA} \times 100$ , where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.