Question

which graph represents the solution set of the inequality -9 > x?
options are four number lines with different markings.

Explanation:

Step1: Analyze the inequality

The inequality is \(-9 > x\), which can be rewritten as \(x < -9\). This means \(x\) takes all values less than \(-9\).

Step2: Analyze the number line features

• For an inequality with \(<\) (not including the endpoint), we use an open circle at the endpoint (\(-9\) here).
• The values less than \(-9\) are to the left of \(-9\) on the number line, so the arrow should point to the left.

Now, let's check the options:

• First option: Open circle at \(-9\), arrow to the left (correct direction for \(x < -9\)).
• Second option: Closed circle (used for \(\leq\) or \(\geq\)), so incorrect.
• Third option: Arrow to the right (represents \(x > -9\)), incorrect.
• Fourth option: Closed circle and arrow to the right, incorrect.

Answer:

The first graph (with open circle at -9 and arrow to the left, labeled with -13, -12, -11, -10, -9, -8, -7 on the number line)