Final answer:
Rewriting the inequalities using the Asymmetric property, the first inequality g-4>29 becomes 33 < g, and the second inequality 2u ≥ 12 becomes 6 ≤ u. The Asymmetric property helps us to reverse inequalities while maintaining their truths.
Step-by-step explanation:
When looking at the question of rewriting inequalities using the Asymmetric property of inequality, it is essential to understand that this property states that for any two real numbers (or variables), if a is less than b, then it is not possible for b to also be less than a. In mathematical terms, if a < b, then b > a. It's an established characteristic of order relations in mathematics. Applying this definition, let's examine the two inequalities provided.
Inequality I
The first inequality given is g-4>29. We can rewrite and solve for g:
- Add 4 to both sides to isolate g: g > 33.
Using the Asymmetric property, we can express this as 33 < g.
Inequality II
The second inequality given is 2u ≥ 12. We can rewrite and solve for u:
- Divide both sides by 2 to isolate u: u ≥ 6.
Applying the Asymmetric property for inequalities that include "greater than or equal to," we can express this as 6 ≤ u.
Remember, when using the Asymmetric property for inequalities, the property only strictly holds for strict inequalities (< and >). For inequalities that include 'greater than or equal to' (≥) or 'less than or equal to' (≤), we can still reverse the order but must keep in mind the inclusive nature of the inequality.