Question

solve for (x): (-8x \le 24)

(x \ge 3)
(x \le -3)
(x = -3)
(x \ge -3)

Explanation:

Isolate the variable

Using the Linear Equations knowledge point

$$ -8x \le 24 $$

Divide both sides by \(-8\). Since we divide by a negative number, we must reverse the inequality sign:

$$ x \ge \frac{24}{-8} $$

$$ x \ge -3 $$

Match with the correct graph

Using the Graphing Inequalities and Number Line Representation knowledge points

$$ x \ge -3 $$

• The inequality symbol \(\ge\) means we use a solid circle at \(-3\) to show that \(-3\) is included.
• The "greater than or equal to" direction means the arrow must point to the right.
• This matches the fourth option: \(x \ge -3\) with a solid dot at \(-3\) and a blue arrow pointing to the right.

Answer:

• (A) \(x \ge 3\) with a solid dot at \(3\) and arrow pointing right
• (B) \(x \le -3\) with a solid dot at \(-3\) and arrow pointing left
• (C) \(x = -3\) with a single solid dot at \(-3\)
• (D) \(x \ge -3\) with a solid dot at \(-3\) and arrow pointing right (Correct answer)