Write the interval notation corresponding to the set notation

{x | x < –7}

Could it be (-7]

The simple interval notation requires the lower and upper limites separated by a comma. Also, parenthese indicate the limites are excluded.

So the example given will be translated to
(-infinity, -7)
One or more square brackets will replace the parenthesis if the limit is included.
For example, [-5,5] will start from -5 inclusively to +5, also inclusively.
Simple intervals may be joined together using the logical 'and' or 'or' operators.
See:
http://www.sosmath.com/algebra/inequalities/ineq02/ineq02.html

Thank you for your help!

No, the correct interval notation for the set notation {x | x < -7} would be (-∞, -7).

To understand why, let's break it down:

The set notation {x | x < -7} represents the set of all real numbers x for which x is less than -7. This means that any value of x that is smaller than -7 would be included in this set.

In interval notation, we use parentheses to indicate that the endpoint is not included in the set. Since the inequality is strict (x < -7), the endpoint -7 itself is not included. Hence, we use a parentheses on the left side.

On the other hand, we use the symbol "∞" (infinity) to represent numbers that continue indefinitely. Since there is no upper bound given in the set notation, we use the symbol "∞" on the right side. Again, we use parentheses to indicate that it is not included in the set.

Therefore, the correct interval notation for this set would be (-∞, -7).