Question

introduction to compound inequalities
which compound inequality could be represented by the graph?
number line from -5 to 5
$x \leq -1$ or $x \geq 0$
$-2 \leq x \leq -1$
$-4 \leq x \leq 4$
$x \leq 3$ or $x \geq -1$

Explanation:

Step1: Analyze the graph (assuming the graph has a segment from -2 to -1, closed circles)

The graph likely shows a line segment between -2 and -1, including both endpoints. So we check each option:

• Option 1: \(x \leq -1\) or \(x \geq 0\) – this would be two separate regions, not a segment between -2 and -1.
• Option 2: \(-2 \leq x \leq -1\) – this is a segment from -2 to -1, including both, matching the assumed graph.
• Option 3: \(-4 \leq x \leq 4\) – this is a wide segment from -4 to 4, not matching.
• Option 4: \(x \leq 3\) or \(x \geq -1\) – this covers most of the number line, not a segment between -2 and -1.

Answer:

\(-2 \leq x \leq -1\) (the second option, e.g., if options are labeled A: \(x \leq -1\) or \(x \geq 0\), B: \(-2 \leq x \leq -1\), C: \(-4 \leq x \leq 4\), D: \(x \leq 3\) or \(x \geq -1\), then the answer is B. \(-2 \leq x \leq -1\))