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8. Solve : \(2(x-1){<}x+5,\) \(3(x + 2) > 2-x \) and represent the solution graphically on number line.

Linear Inequalities

Miscellaneous Exercise

Ncert Solutions class 11 Linear Inequalities Miscellaneous Exercise
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Class 11

Linear Inequalities

Miscellaneous Exercise

1. Solve : \(2\le 3x-4\le 5\).

2. Solve : \(6≤-3(2x-4)<12\).

3. Solve : \(-3≤4-{7x \over 2}≤18\).

4. Solve : \(-15<{3(x-2) \over 5}≤0\).

5. Solve : \(-12<4-{3x \over -5}≤2\).

6. Solve : \(7≤{(3x+11)\over 2}≤11\).

7. Solve : \(5x+1>-24\) \(,5x-1<24 \) and represent the solution graphically on number line.

8. Solve : \(2(x-1){<}x+5,\) \(3(x + 2) > 2-x \) and represent the solution graphically on number line.

9. Solve : \(3x-7>2(x-6)\)\(,6-x>11-2x \) and represent the solution graphically on number line.

10. Solve : \(5(2x-7)-3(2x+3)≤0\) \(,2x+19≤6x+47\) and represent the solution graphically on number line.

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 \(F={9 \over 5}C+32 \) ?

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?

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?

14. IQ of a person is given by the formula \(IQ={MA \over CA}×100\), 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.