#### Linear Inequalities

#### Exercise 5.1

5. Solve for x: 4x + 3 < 5x + 7.

6. Solve for x: 3x – 7 > 5x – 1.

7. Solve for x: 3(x – 1) ≤ 2 (x – 3).

8. Solve for x: 3 (2 – x) ≥ 2 (1 – x).

9. Solve for x: \(x+\frac{x}{2}+\frac{x}{3}<11\).

10. Solve for x: \(\frac{x}{3}>\frac{x}{2}+1\).

11. Solve for x: \(\frac{3(x-2)}{5}\le\frac{5(2-x)}{3}\).

12. Solve for x: \(\frac{1}{2}(\frac{3x}{5}+4)\ge\frac{1}{3}(x-6)\).

13. Solve for x: 2 (2x + 3) – 10 < 6 (x – 2).

14. Solve for x: 37 – (3x + 5) ≥ 9x – 8 (x – 3).

15. Solve for x: \(\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}\).

16. Solve for x: \(\frac{(2x-1)}{3}\ge\frac{(3x-2)}{4}-\frac{(2-x)}{5}\).

#### Linear Inequalities

#### Miscellaneous Exercise

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

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.

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