The set $\{x \, | \, x \leq -5\}$ in interval notation is:

$(-\infty, -5]$

Explanation:

• The inequality $x \leq -5$ means $x$ includes all values less than or equal to $-5$.
• The square bracket $[\,]$ indicates that $-5$ is included in the set.
• The parenthesis $(\,)$ around $-\infty$ indicates that $-\infty$ is not an actual number and cannot be included in the set.

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5 Related Questions:

1. How would the set $\{x \, | \, x > -5\}$ look in interval notation?
2. What is the difference between $[-5, \infty)$ and $(-5, \infty)$?
3. How do you graph $\{x \, | \, x \leq -5\}$ on a number line?
4. Can $-\infty$ or $\infty$ ever be included in interval notation?
5. How would $\{x \, | \, -10 < x \leq -5\}$ look in interval notation?

Tip:

Always match the inequality symbols ($<, \leq, >, \geq$) with the correct brackets $(, [)$ when converting to interval notation!