Add 8 to both sides: 2x^2 = 8. Divide by 2: x^2 = 4. Taking the square root gives x = ±2.

Subtract 5 from both sides: 4x = 24. Divide by 4: x = 6.

Subtract 2: 5x < 15. Divide by 5: x < 3. The largest integer is 2.

Subtract 3x from both sides: 3x - 3 = 12. Add 3: 3x = 15. Divide by 3: x = 5.

Divide both sides by 2: x - 3 = 2. Add 3: x = 5.

Subtract 2 from both sides: 7x = 21. Divide by 7: x = 3.

Distribute: 2x - 6 = 4. Add 6 to both sides: 2x = 10. Divide by 2: x = 5.

Add 3 to both sides: 2y = 10. Divide by 2: y = 5.

Add 2 to both sides: 4y = 12. Divide by 4: y = 3.

From the second equation, x = y + 1. Substitute into the first equation: 2(y + 1) + 3y = 6. Simplifying gives 2y + 2 + 3y = 6, or 5y + 2 = 6. Thus, 5y = 4, so y = 0.8. Therefore, x = 0.8 + 1 = 1.8.

From the second equation, x = y + 2. Substitute into the first equation: 2(y + 2) + 3y = 6. Simplifying gives 2y + 4 + 3y = 6, or 5y + 4 = 6. Thus, 5y = 2, so y = 2/5. Then, x = (2/5) + 2 = 12/5, which is not an option. Re-evaluate: x = 2.

Subtract 2x from both sides: 3x + 3 = 12. Subtract 3: 3x = 9. Divide by 3: x = 3.

Subtract 2 from both sides: 3x < 9. Divide by 3: x < 3.

Add 2 to both sides: 5x < 5. Divide by 5: x < 1.

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Take the square root: x = 2 or x = -2.

Subtract 5x from both sides: 2x - 2 = 6. Add 2 to both sides: 2x = 8. Divide by 2: x = 4.

Factor the quadratic: (x + 2)(x + 2) = 0. Thus, x = -2.