Case context: Start with the true inequality $5 < 9$. Add $4$ to both sides to get $9 < 13$. The inequality symbol did not change direction.

Question: Read the case below, then answer the questions that follow.

Sample answer: The Addition Property of Inequality explains this. It states that for any numbers $a$, $b$, and $c$: if $a < b$, then $a + c < b + c$. Adding the same number to both sides of an inequality never changes the direction of the inequality symbol.

Key points:

• Identifies the property as the Addition Property of Inequality
• States the formal rule: if $a < b$, then $a + c < b + c$ (and similarly for $>$, $\leq$, $\geq$)
• Explains that adding the same quantity to both sides does not change the direction of the inequality symbol
• Connects the rule back to the example: $5 < 9$ becomes $9 < 13$ after adding $4$ to both sides

Rubric: Full credit: names the Addition Property of Inequality, states the formal definition (if $a < b$, then $a + c < b + c$), and explains that the inequality symbol keeps the same direction. Partial credit: names the property but gives an incomplete or incorrect definition. No credit: names an unrelated property or gives no definition.