Question

graph $x \leq -1$.
how do i graph the inequality?

Explanation:

Step1: Identify the critical point

The inequality is \( x \leq -1 \), so the critical point is \( x = -1 \).

Step2: Determine the circle type

Since the inequality is "less than or equal to", we use a closed (filled) circle at \( x = -1 \) to indicate that \( -1 \) is included in the solution set.

Step3: Determine the direction of the line

For \( x \leq -1 \), we shade (or draw the line) to the left of \( -1 \) because we want all values of \( x \) that are less than or equal to \( -1 \).

Answer:

1. Draw a closed (filled) circle at \( x = -1 \) on the number line.
2. Draw a line extending to the left from the closed circle to represent all values of \( x \) that satisfy \( x \leq -1 \).