Question

graph the inequality on a number line. then write the solution in interval notation. \\(\\{x|-3 < x < 7\\}\\) select the correct graph below. now enter the solution in interval notation.

Explanation:

Step1: Analyze the inequality

The inequality is \(-3 < x < 7\). This means \(x\) is greater than \(-3\) and less than \(7\). On a number line, we use open circles (since the inequality is strict, not including \(-3\) and \(7\)) and shade the region between \(-3\) and \(7\).

Looking at the graphs:

• Graph A: Shades from \(-7\) to \(3\), incorrect.
• Graph B: Has a closed circle at \(3\) and \(7\), incorrect (we need open circles).
• Graph C: Shades from \(-3\) (open circle) to \(7\) (open circle), which matches \(-3 < x < 7\).
• Graph D: Shades from \(-3\) (open circle) to the right indefinitely, incorrect.

So the correct graph is C.

Step2: Write in interval notation

For the inequality \(-3 < x < 7\), in interval notation, we use parentheses (since the endpoints are not included) and write it as \((-3, 7)\).

Answer:

The correct graph is C. The solution in interval notation is \((-3, 7)\).