Question

graph the set \\{x \mid -2 < x < 6\\} on the number line. then, write the set using interval notation.

Explanation:

Graphing on the Number Line:

1. Locate the points -2 and 6 on the number line.
2. Since the inequality is \( -2 < x < 6 \) (strictly less than, not less than or equal to), we use open circles (hollow dots) at -2 and 6.
3. Draw a line segment connecting the open circles at -2 and 6 to represent all the numbers between -2 and 6.

Interval Notation:

For an inequality of the form \( a < x < b \) (where \( a \) and \( b \) are real numbers and \( a < b \)), the interval notation is \( (a, b) \). Here, \( a = -2 \) and \( b = 6 \), so the interval notation is \( (-2, 6) \).

Final Answer for Interval Notation:

\( (-2, 6) \)

(Note: For the graph, as described, place open circles at -2 and 6 and shade the region between them on the number line provided.)

Answer:

Graphing on the Number Line:

1. Locate the points -2 and 6 on the number line.
2. Since the inequality is \( -2 < x < 6 \) (strictly less than, not less than or equal to), we use open circles (hollow dots) at -2 and 6.
3. Draw a line segment connecting the open circles at -2 and 6 to represent all the numbers between -2 and 6.

Interval Notation:

For an inequality of the form \( a < x < b \) (where \( a \) and \( b \) are real numbers and \( a < b \)), the interval notation is \( (a, b) \). Here, \( a = -2 \) and \( b = 6 \), so the interval notation is \( (-2, 6) \).

Final Answer for Interval Notation:

\( (-2, 6) \)

(Note: For the graph, as described, place open circles at -2 and 6 and shade the region between them on the number line provided.)