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“Hard times don’t create heroes. It is during the hard times when the ‘hero’ within us is revealed.” – Bob Riley

Basics of Inequalities, Strict and Slack inequalities

Working with inequalities: Adding positive or negative numbers Subtracting positive or negative numbers Multiplying by positive or negative numbers Dividing by positive or negative numbers

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Representing Real numbers in form of open intervals and closed intervals

NCERT Exercise 6.1

Question 1. Solve \( 24x < 100 \), when 

(i) x is a natural number.
(ii) x is an integer.

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Question 2. Solve – 12x > 30, when
(i) x is a natural number.
(ii) x is an integer.

Question 3. Solve 5x – 3 < 7, when
(i) x is an integer.
(ii) x is a real number.

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Question 4. Solve 3x + 8 >2, when
(i) x is an integer.
(ii) x is a real number.

Solve the inequalities in Exercises 5 to 16 for real x.

Question 5. \(4x+3<5x+7\)

Question 6. \(3x-7>5x-1\)

Question 7. \(3(x-1) \le 2 (x-3)\)

Question 8. \(3(2-x) \ge 2(1-x)\)

Question 9. \(x + \frac{x}{2}+\frac{x}{3}<11\)

Question 10. \(\frac{x}{3}>\frac{x}{2}+1\)

Question 11. \(\frac{3(x-2)}{5} \le \frac{5(2-x)}{3}\)

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Question 12. \(\frac{1}{2} \left ( \frac{3x}{5} + 4 \right ) \ge \frac{1}{3} (x-6)\)

Question 13. \(2 (2x + 3) – 10 < 6 (x – 2)\)

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Question 14. \(37 – (3x + 5) > 9x – 8 (x – 3)\)

Question 15. \(\frac{x}{4}< \frac{(5x-2)}{3} – \frac{(7x-3)}{5}\)

Question 16. \(\frac{(2x-1)}{3} \ge \frac{(3x-2)}{4} – \frac{(2-x)}{5}\)

Solve the inequalities in Exercises 17 to 20 and show the graph of the solution in each case on number line

Question 17. \(3x-2<2x+1\)

Question 18. \(5x-3 \ge 3x-5\)

Question 19. \(3(1-x) < 2(x+4)\)

Question 20. \(frac{x}{2} \ge \frac{(5x-2)}{3} – \frac{(7x-3)}{5}\)

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