Question

what inequality does this number line show? write your answer starting with x (for example, x < 3).

Explanation:

Step1: Analyze the number line

The red line on the number line is shaded to the left of 1, and the arrow at 1 is a closed (filled) circle? Wait, no, looking at the number line, the red line goes up to 1 with a closed or open? Wait, the number line has marks at -3, -2, -1, 0, 1, 2. The red arrow is going towards the left, ending at 1 with a filled (closed) dot? Wait, no, the original number line: the red line is from left (negative direction) up to 1, with the arrow at 1 pointing to the left? Wait, no, the number line's red part: the arrow is on the left side, and the endpoint at 1 is a closed circle? Wait, actually, in the number line, if the red line includes 1 and goes to the left, that means \( x \) is less than or equal to 1? Wait, no, wait the number line: the red line is from the left (all numbers less than or equal to 1?) Wait, the number line has the red line with the endpoint at 1, and the arrow is towards the left (decreasing direction). Wait, the standard number line: a closed dot at 1 means inclusive, and the line going left means all numbers less than or equal to 1? Wait, no, wait the original image: the red line is shaded up to 1, with the arrow at 1 pointing to the left? Wait, maybe I missee. Wait, the number line: the marks are -3, -2, -1, 0, 1, 2. The red line is from the left (so all numbers to the left of 1, including 1? Wait, the endpoint at 1: is it a closed circle (filled) or open? In the image, the arrow at 1 is a closed circle (filled), so that means \( x \leq 1 \)? Wait, no, wait the user's example is \( x < 3 \). Wait, maybe the number line has a closed dot at 1, so the inequality is \( x \leq 1 \)? Wait, no, let's check again. Wait, the number line: the red line is shaded to the left of 1, with the endpoint at 1 being a closed dot (so including 1), so the inequality is \( x \leq 1 \)? Wait, no, maybe the dot is open? Wait, the original image: the number line's red part: the endpoint at 1 is a closed circle (filled), so the inequality is \( x \leq 1 \). Wait, but let's confirm. If the dot is closed, it's \( \leq \) or \( \geq \); if open, \( < \) or \( > \). So in this case, the red line is from the left (all numbers less than or equal to 1), so \( x \leq 1 \).

Wait, maybe I made a mistake. Let's re-examine: the number line has the red arrow going towards the left, ending at 1 with a closed (filled) circle. So the solution set is all real numbers \( x \) such that \( x \) is less than or equal to 1. So the inequality is \( x \leq 1 \).

Step2: Write the inequality

Based on the number line, the shaded region includes 1 and all numbers to the left of 1, so the inequality is \( x \leq 1 \).

Answer:

\( x \leq 1 \)