Which ordered pairs represent solutions to the inequality 3y ≤ -x - 12?
Understand the Problem
The question is asking which of the provided ordered pairs are solutions to the inequality 3y ≤ -x - 12. This involves substituting each pair into the inequality and checking for validity.
Answer
The solution is the ordered pair \((0, -4)\).
Answer for screen readers
The ordered pair ((0, -4)) is a solution to the inequality (3y \leq -x - 12).
Steps to Solve
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Understanding the Inequality
We need to determine whether each ordered pair ((x, y)) satisfies the inequality (3y \leq -x - 12). -
Substituting Ordered Pairs
Substitute each ordered pair into the inequality and check if it holds.-
For ((-5, -5)): [ 3(-5) \leq -(-5) - 12 \Rightarrow -15 \leq 5 - 12 \Rightarrow -15 \leq -7 \text{ (False)} ]
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For ((0, -4)): [ 3(-4) \leq -(0) - 12 \Rightarrow -12 \leq 0 - 12 \Rightarrow -12 \leq -12 \text{ (True)} ]
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For ((0, 0)): [ 3(0) \leq -(0) - 12 \Rightarrow 0 \leq 0 - 12 \Rightarrow 0 \leq -12 \text{ (False)} ]
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For ((1, 7)): [ 3(7) \leq -(1) - 12 \Rightarrow 21 \leq -1 - 12 \Rightarrow 21 \leq -13 \text{ (False)} ]
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Validating Results
From our calculations, only the ordered pair ((0, -4)) satisfies the inequality.
The ordered pair ((0, -4)) is a solution to the inequality (3y \leq -x - 12).
More Information
This inequality represents a region in the coordinate plane. The pair ((0, -4)) lies within this region, which can be depicted graphically.
Tips
- A common mistake is miscalculating the inequality sign; ensure you understand when to flip the sign (not applicable here since numbers are positive or negative).
- Forgetting to multiply the (y) term correctly can lead to incorrect conclusions.
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