Question

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inequality statement: ( x geq -6 ) and ( x geq 5 )

Explanation:

Step1: Analyze the compound inequality

The inequality is \( x \geq -6 \) and \( x \geq 5 \). For a compound inequality with "and", we take the intersection of the two solution sets. The intersection of \( x \geq -6 \) (all numbers greater than or equal to -6) and \( x \geq 5 \) (all numbers greater than or equal to 5) is \( x \geq 5 \) (since 5 is greater than -6, the stricter condition is \( x \geq 5 \)).

Step2: Analyze each graph

• First graph: Has a closed dot at -6 and extends to the right. This represents \( x \geq -6 \), not \( x \geq 5 \).
• Second graph: Has a closed dot at 5 and extends to the right. This represents \( x \geq 5 \), which matches our solution.
• Third graph: Has closed dots at -6 and 5 and extends between them. This represents \( -6 \leq x \leq 5 \), which is not our solution.

Answer:

The Middle Graph (the second graph with the closed dot at 5 and extending to the right)