Question

write an inequality for graph 2:

graph 1
graph 2
graph 3
graph 4

\\(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: A solid (closed) red circle is plotted at \(x = -2\).
• Right boundary: An open circle is plotted at \(x = 5\).

Determine the inequality signs

Using the Inequality Symbols knowledge point

• The solid circle at \(-2\) means \(-2\) is included: \(\ge\) or \(\le\).
• The open circle at \(5\) means \(5\) is excluded: \(>\) or \(<\\).

Write the 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)
• \(x \le -2\text{ or } x > 5\)