Rewrite the following as an inequality statement.
$(-\infty ,2]$

• A. $x\le 2$
• B.
• C. $x\ge 2$
• D. $x>2$

Answer: (A)

Verified step by step guidance

1. Identify the interval notation given: \(\left(-\infty, 2\right]\). This represents all numbers starting from negative infinity up to and including 2.
2. Recall that \(\left(-\infty, 2\right]\) means the values are less than or equal to 2, because the bracket ']' indicates inclusion of the endpoint 2.
3. Translate the interval into an inequality by expressing that the variable \(x\) is less than or equal to 2.
4. Write the inequality as \(x \leq 2\) to represent all values from negative infinity up to and including 2.
5. Confirm that this inequality matches the interval notation and correctly describes the set of numbers in the interval.