Question 41

x < 1

The solution to the inequality 3x + 6(3 - x) < 5(x + 2) is x < 1, indicating that x must be less than 1 to satisfy the inequality.

A) x > 1

This option is incorrect because if x were greater than 1, the left side of the inequality would yield a larger value than the right side, violating the condition of the inequality.

B) x < 1

This option is correct as it aligns with the solution derived from the inequality. When x is less than 1, the inequality holds true, confirming that this range satisfies the original equation.

C) x = 1

This option is incorrect because substituting x = 1 into the inequality does not satisfy the condition. It results in an equality rather than a strict inequality, which does not fulfill the requirement of being less than.

D) There is no solution.

This option is also incorrect. The inequality does have a solution, as shown in the analysis, which indicates that there is a range of values (specifically, all values less than 1) that satisfy the inequality.

Conclusion

The correct answer, x < 1, effectively captures the range of values that satisfy the inequality, while all other options either suggest incorrect ranges or imply that no solution exists. Thus, the analysis clearly demonstrates that x must indeed be less than 1 to meet the requirements of the original expression.