Question

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in set - builder notation is \\( \\{ x | x < 5.7 \\} \\) (use integers or decimals for any numbers in the expression )
b. the solution set is all real numbers.
c. there is no solution.
choose the correct graph below.

Explanation:

Step1: Analyze interval notation

The interval \((-\infty,5.7)\) means all real numbers \(x\) such that \(x < 5.7\). In set - builder notation, this is written as \(\{x|x < 5.7\}\).

Step2: Analyze graph options

For the inequality \(x<5.7\), the graph should have an open circle at \(x = 5.7\) (since \(5.7\) is not included in the solution set) and the arrow should point to the left (towards \(-\infty\)).

Answer:

A. The solution set in set - builder notation is \(\{x|x < 5.7\}\) and the correct graph is option C (assuming option C has an open circle at \(5.7\) and the arrow points to the left).