Question

graphing compound inequalities
which graph represents the inequality ( x leq -2 ) or ( x geq 0 )?
four number line graphs with -4, -3, -2, -1, 0, 1 marked, different shading/arrow directions, and selection circles (one with a blue check)

Explanation:

Step1: Analyze \( x \leq -2 \)

For \( x \leq -2 \), we use a closed circle at \(-2\) (since the inequality is "less than or equal to") and shade to the left (towards negative infinity).

Step2: Analyze \( x \geq 0 \)

For \( x \geq 0 \), we use a closed circle at \( 0 \) (since the inequality is "greater than or equal to") and shade to the right (towards positive infinity).

Step3: Match with the graphs

Now we check each graph:

• First graph: Closed circles at \(-2\) and \(0\), shading left of \(-2\) and right of \(0\) – this matches our analysis.
• Second graph: Closed circles but shading between \(-2\) and \(0\) – incorrect.
• Third and fourth graphs: Open circles – incorrect (since our inequalities have "or equal to").

Answer:

The first graph (with closed circles at -2 and 0, shading left of -2 and right of 0)