Question 4

x < 4

To solve the inequality 8 - 2x > 2x - 8, we first combine like terms, leading to the equivalent statement x < 4.

A) x > -4

This option is incorrect because it suggests that x can take values greater than -4, which does not satisfy the original inequality. The solution derived from the inequality indicates that x must be less than 4, not greater than -4.

B) x > -2

Option B is also incorrect as it implies that x can be any value greater than -2. However, the solution to the inequality shows that x must be less than 4, making this option invalid.

C) x < 2

This choice is incorrect as it restricts x to values less than 2. While it is true that values less than 2 satisfy the original inequality, it does not encompass all values that satisfy x < 4, which is a broader solution.

D) x < 4

This option is correct as it directly reflects the simplification of the original inequality. By rearranging the terms appropriately, we find that x must indeed be less than 4 to satisfy the inequality.

Conclusion

The correct answer, x < 4, accurately represents the solution to the inequality derived from the original expression. All other options fail to reflect the correct relationship established by the manipulation of the inequality, either suggesting a range that does not encompass all valid solutions or contradicting the derived condition.