Question

Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]

• A. \( x \leq -\frac{38}{12} \)
• B. \( x > -\frac{38}{12} \)
• C. \( x > \frac{38}{12} \)
• D. \( x \leq \frac{38}{12} \)

Hint:

When dividing or multiplying by a negative number in an inequality, always reverse the inequality sign.

Answer 1

The Correct Option is C

We are asked to solve the inequality \( -12x > 38 \). 
Step 1: Isolate \( x \) To isolate \( x \), we divide both sides of the inequality by \( -12 \), but remember that dividing or multiplying by a negative number reverses the inequality: \[ x < -\frac{38}{12} \] Simplify \( \frac{38}{12} \): \[ x < -\frac{19}{6} \] Since \( x \in \mathbb{N} \) (natural numbers), the smallest integer greater than \( -\frac{19}{6} \) is \( -3 \). Therefore, the solution set is \( x > 3 \). Hence, the correct answer is \( x > \frac{38}{12} \).