3x + 6(3 - x) < 5(x + 2) What is the solution to the inequality shown?

Rationale

x < 1

To solve the inequality \(3x + 6(3 - x) < 5(x + 2)\), we simplify and isolate \(x\), which leads to the conclusion that \(x\) must be less than 1.

A (x > 1) YOUR ANSWER

This choice suggests that \(x\) is greater than 1, which contradicts the results of the inequality. Upon solving, we find that the values greater than 1 do not satisfy the original inequality, indicating that this option is incorrect.

B (x < 1) CORRECT

This choice accurately reflects the solution to the inequality. After simplifying the expression and isolating \(x\), we find that all values of \(x\) less than 1 satisfy the inequality, making this the correct answer.

C (x = 1) YOUR ANSWER

This choice implies that \(x\) equals 1, which does not satisfy the original inequality as it results in a false statement. When substituting \(x = 1\) back into the inequality, it leads to an equality rather than a true inequality, hence it is not a solution.

D (There is no solution.) YOUR ANSWER

This choice suggests that the inequality has no valid solutions. However, upon solving the inequality, we find that there are indeed solutions within the range of \(x < 1\). Thus, this statement is incorrect.

Conclusion

The correct solution to the inequality \(3x + 6(3 - x) < 5(x + 2)\) is \(x < 1\). This result indicates that any value of \(x\) that is less than 1 will satisfy the inequality, while all other options either contradict this conclusion or misinterpret the nature of the inequality.

3x + 6(3 - x) < 5(x + 2) What is the solution to the inequality shown?

x < 1

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