Solve the compound inequality. Express the answer in interval notation.
(A) $\frac{x}{3}>2$ or

• A. $(-\infty ,6)\cup (6,\infty )$
• B. $(-\infty ,1)\cup (6,\infty )$
• C. $(-\infty ,1.5)\cup (6,\infty )$
• D. $(-\infty ,2)\cup (5,\infty )$

Answer: (B)

Verified step by step guidance

1. Identify the two inequalities given in the compound inequality: \( \frac{x}{3} > 2 \) or \( 4x + 1 < 5 \).
2. Solve the first inequality \( \frac{x}{3} > 2 \) by multiplying both sides by 3 to isolate \( x \): \( x > 2 \times 3 \).
3. Solve the second inequality \( 4x + 1 < 5 \) by first subtracting 1 from both sides: \( 4x < 5 - 1 \), then dividing both sides by 4 to isolate \( x \): \( x < \frac{4}{4} \).
4. Since the compound inequality uses 'or', combine the solutions by taking the union of the two solution sets: \( x > 6 \) or \( x < 1 \).
5. Express the combined solution in interval notation as the union of two intervals: \( (-\infty, 1) \cup (6, \infty) \).