Question

which graph corresponds to the inequality \\(x \le -6\\)?

Explanation:

Identify the inequality components

Using the Linear Equations knowledge point

$$ x \le -6 $$

The boundary value is \(-6\). The inequality symbol is \(\le\) (less than or equal to).

Determine the circle type

The inequality symbol \(\le\) includes "or equal to." This means \(-6\) is part of the solution set, which requires a solid (filled-in) circle at \(-6\).

Determine the arrow direction

The inequality symbol \(\le\) represents values less than or equal to \(-6\). On a number line, values less than \(-6\) lie to the left, so the arrow must point to the left.

Match with the given options

• Option 1: Solid circle at \(-6\), arrow pointing left.
• Option 2: Open circle at \(-6\), arrow pointing left.
• Option 3: Open circle at \(-6\), arrow pointing right.
• Option 4: Solid circle at \(-6\), arrow pointing right.

The correct match is the first option.

Answer:

• (A) Solid circle at \(-6\) with arrow pointing left (Correct answer)
• (B) Open circle at \(-6\) with arrow pointing left
• (C) Open circle at \(-6\) with arrow pointing right
• (D) Solid circle at \(-6\) with arrow pointing right