Express the given set in interval notation and graph.
$\left\lbrace\right.$$x$ $|$$x\le7$$\}$

• A. (−∞,7]
• B. [−∞,7]
• C. (−∞,7)
• D. [7, ∞)

Answer: (A)

Verified step by step guidance

1. Identify the inequality given in the set notation: \( x \leq 7 \). This means all values of \( x \) are less than or equal to 7.
2. Understand that the interval notation for \( x \leq 7 \) is \((-\infty, 7]\). The parenthesis \((-\infty\) indicates that infinity is not a number and cannot be included, while the bracket \([7]\) indicates that 7 is included in the set.
3. Examine the graph provided: The graph shows a line extending to the left from 7, with a solid dot at 7, indicating that 7 is included in the interval.
4. Recognize that the correct interval notation based on the graph is \((-\infty, 7]\), which matches the inequality \( x \leq 7 \).
5. Choose the correct answer from the options given: \((-\infty, 7]\) is the correct interval notation for the set \( \{ x \mid x \leq 7 \} \).