Select the correct choice below and, if necessary, fill out the answer box to complete your choice.
A. The solution set in set-builder notation is \{x \mid \square\}.
(Type an inequality or a compound inequality.)
B. The solution set is all real numbers.
C. There is no solution.
Answer (2)
The problem provides the solution set as an interval ( − ∞ , 8 ) .
We express this interval in set-builder notation.
The interval ( − ∞ , 8 ) includes all real numbers less than 8.
Therefore, the solution set in set-builder notation is { x ∣ x < 8 } .
Explanation
Understanding the Problem The solution set is given as the interval ( − ∞ , 8 ) . This interval represents all real numbers less than 8. We need to express this solution set using set-builder notation.
Expressing in Set-Builder Notation In set-builder notation, we describe a set by specifying a condition that its elements must satisfy. In this case, the set consists of all x such that x is less than 8.
Final Answer Therefore, the solution set in set-builder notation is { x ∣ x < 8 } . This means 'the set of all x such that x is less than 8'.
Examples
Understanding intervals and set-builder notation is crucial in many areas of mathematics. For example, when describing the domain or range of a function, we often use intervals or set-builder notation. Imagine you are describing the acceptable range of temperatures for a science experiment. You might say the temperature must be in the interval ( − ∞ , 8 ) degrees Celsius, meaning any temperature less than 8 degrees. Expressing this as { x ∣ x < 8 } provides a clear and concise way to communicate the allowable temperatures.
The solution set in set-builder notation is { x \mid x < 8 }, which indicates all real numbers less than 8. This notation clarifies the condition that must be satisfied for elements in the set. Hence, the selected option is A.
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