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# Lecture - 4 Chapter 6 Linear Inequalities

NCERT Miscellaneous Exercise |

Solve the inequalities in Exercises 1 to 6.

**Question 1.** \(2 ≤ 3x – 4 ≤ 5\)

**Question 2.** \(6 ≤ – 3 (2x – 4) < 12\)

**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.** \(5 (2x – 7) – 3 (2x + 3) ≤ 0 , 2x + 19 ≤ 6x + 47 \)

**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.