Question

write an inequality for graph 2:

\\(x < -2\\) or \\(x > 5\\)
\\(-2 \le x \le 5\\)
\\(-2 \le x < 5\\)
\\(x \le -2\\) or \\(x > 5\\)

Explanation:

Identify the boundary points

Using the Graphing Inequalities knowledge point

• Left boundary: solid circle at \(x = -2\)
• Right boundary: open circle at \(x = 5\)

Determine the interval type

Using the Compound Inequalities knowledge point

• Shaded region is between \(-2\) and \(5\)
• Left boundary is included: \(x \ge -2\)
• Right boundary is excluded: \(x < 5\)

Combine into a compound inequality

Using the Compound Inequalities knowledge point

$$ -2 \le x < 5 $$

Answer:

• \(x < -2\text{ or }x > 5\)
• \(-2 \le x \le 5\)
• \(-2 \le x < 5\) (Correct answer)
• \(x \le -2\text{ or }x > 5\)