Question

which of the following is the graph of this inequality? x ≥ 8 two number lines with markings from 3 to 13, first with open circle at 8, second with closed circle at 8

Explanation:

Step1: Analyze the inequality \( x \geq 8 \)

The inequality \( x \geq 8 \) means that \( x \) can be 8 or any number greater than 8. On a number line, for an inequality with "greater than or equal to" (\(\geq\)), we use a closed (filled - in) circle at the boundary point (since the point 8 is included in the solution set) and an arrow pointing to the right (to represent all numbers greater than 8).

Step2: Analyze the two number lines

• For the first number line: It has an open circle at 8. An open circle is used for inequalities like \( x>8 \) (where 8 is not included), so this does not match the inequality \( x \geq 8 \).
• For the second number line: It has a closed circle at 8 and an arrow pointing to the right, which matches the solution set of \( x \geq 8 \) (including 8 and all numbers greater than 8).

Answer:

The second number line (the one with the closed red circle at 8 and the arrow pointing to the right) is the graph of the inequality \( x \geq 8 \).