Final answer:
The correct inversion of the inequality -x < 34 when dividing by -1 is x > -34, which is not given in the provided options. When handling inequalities, the direction of the inequality sign must be reversed when multiplying or dividing by a negative number.
Step-by-step explanation:
The student is asking about inverting the inequality symbol when dealing with a negative coefficient. In the original inequality, –x < 34, to solve for x one would typically divide both sides by -1 (assuming x is real). Inequalities have a specific behavior when multiplied or divided by a negative number; the inequality sign reverses. Therefore, after dividing both sides by -1, the correct reversal of the inequality would be x > -34.
To address the options given in the question:
- A) -x > 34 is incorrect because it represents a greater-than relationship but does not invert the sign.
- B) -x ≤ 34 is not only incorrect, it introduces the equal-to component unnecessarily.
- C) -x ≥ 34 is not only incorrect, but in the wrong direction entirely.
- D) -x = 34 is not a correct inequality relationship.
None of the options listed are correct; when the inequality -x < 34 is reversed properly by dividing by -1, it should be represented as x > -34, which is not listed. Reversing an inequality when multiplying or dividing by a negative is an essential mathematical concept to understand when solving inequalities.