Question

xample 8: -8 -6 -4 -2 0 2 4 6 8 10

Explanation:

Step1: Identify the points

The number line has two marked points: an open circle at -5 (since it's between -6 and -4, likely -5) and a closed circle at 5 (wait, no, the closed circle is at 5? Wait, the numbers are -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. Wait, the closed circle is at 5? Wait, no, the closed circle is between 4 and 6, so 5? Wait, no, the open circle is at -5 (since -6, -5, -4: the open circle is at -5? Wait, the open circle is at -5 (position between -6 and -4, so -5), and the closed circle is at 5? Wait, no, the closed circle is at 5? Wait, the number line: let's check the positions. The open circle is at -5 (since -6, -5, -4: the open circle is at -5), and the closed circle is at 5? Wait, no, the closed circle is at 5? Wait, the numbers are marked at -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. So the closed circle is at 5? Wait, no, between 4 and 6, so 5? Wait, maybe the open circle is at -5 (since -6, -5, -4: the open circle is at -5), and the closed circle is at 5? Wait, no, the closed circle is at 5? Wait, maybe the inequalities are: open circle at -5 (so \( x < -5 \)) and closed circle at 5 (so \( x \geq 5 \))? Wait, no, the arrows: the left arrow is from the open circle, and the right arrow is from the closed circle. Wait, the open circle is at -5 (let's confirm: the open circle is at -5, since -6, -5, -4: the open circle is at -5), and the closed circle is at 5 (between 4 and 6, so 5). So the left arrow (from open circle) is \( x < -5 \), and the right arrow (from closed circle) is \( x \geq 5 \)? Wait, no, the open circle is at -5, so the left arrow is \( x < -5 \), and the closed circle is at 5, so the right arrow is \( x \geq 5 \). Wait, but maybe the open circle is at -5 and the closed circle is at 5. So the solution is \( x < -5 \) or \( x \geq 5 \).

Wait, maybe I misread. Let's check again. The open circle is at -5 (position: -6, -5, -4: the open circle is at -5), and the closed circle is at 5 (position: 4, 5, 6: the closed circle is at 5). So the left arrow (from open circle) is \( x < -5 \), and the right arrow (from closed circle) is \( x \geq 5 \). So the solution set is \( x < -5 \) or \( x \geq 5 \).

Step2: Write the inequalities

The open circle at -5 means \( x < -5 \) (since open circle is exclusive), and the closed circle at 5 means \( x \geq 5 \) (closed circle is inclusive). The arrows: left from open circle ( \( x < -5 \) ) and right from closed circle ( \( x \geq 5 \) ). So the compound inequality is \( x < -5 \) or \( x \geq 5 \).

Answer:

The solution to the inequality represented by the number line is \( x < -5 \) or \( x \geq 5 \) (assuming the open circle is at -5 and closed at 5; if the closed circle is at 5, then the solution is \( x < -5 \) or \( x \geq 5 \)). Wait, maybe the open circle is at -5 and closed at 5. So the answer is \( x < -5 \) or \( x \geq 5 \).