Verified Answer :

  • Analyze the inequality \(x > -2\) to identify values greater than \(-2\).
  • Substitute each candidate value \(\{-1, -4, -3, -2\}\) into the inequality.
  • Observe that only \(-1\) satisfies the condition \(-1 > -2\).
  • The correct value is \(\boxed{-1}\).

Explanation

  1. Problem Analysis

To determine which value from the set \(\{-1, -4, -3, -2\}\) satisfies the inequality \(x > -2\), we must check each value individually to see if it makes the statement true. The inequality \(x > -2\) specifies that any value greater than \(-2\) on the number line will satisfy the condition. Values to the right of \(-2\) are greater than \(-2\), while values to the left are less than \(-2\).

  1. Evaluating Candidate Values

We now evaluate each candidate value:

  1. For \(x = -1\): The inequality becomes \(-1 > -2\). Since \(-1\) is located to the right of \(-2\) on the number line, this statement is true.
  2. For \(x = -4\): The inequality becomes \(-4 > -2\). Since \(-4\) is located to the left of \(-2\) on the number line, this statement is false.
  3. For \(x = -3\): The inequality becomes \(-3 > -2\). Since \(-3\) is located to the left of \(-2\) on the number line, this statement is false.
  4. For \(x = -2\): The inequality becomes \(-2 > -2\). This statement is false because \(-2\) is equal to \(-2\), not strictly greater than it.
  1. Conclusion

After checking each option, we find that only \(x = -1\) satisfies the inequality \(x > -2\). Therefore, \(-1\) is the only solution provided in the list. The final answer is \(\boxed{-1}\).

Examples

Understanding inequalities is essential in everyday life when dealing with thresholds. For example, consider a bank account requirement where you must maintain a balance of more than \(\$ -2\) (in terms of allowed debt). If your current account balances are represented by the set \(\{-1, -4, -3, -2\}\), checking which values satisfy the condition \(x > -2\) helps determine which balance levels are acceptable under the account policy. This logic applies to any scenario involving minimum requirements or physical constraints, such as temperature ranges or speed limits.

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