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

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

Answer: (B)

Verified step by step guidance

1. Start by writing down the two inequalities separately: \( \frac{x}{3} > 2 \) and \( 4x + 1 < 5 \).
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', the solution is the union of the two solution sets: \( x > 6 \) or \( x < 1 \).
5. Express the solution in interval notation by combining the intervals for \( x < 1 \) and \( x > 6 \) as \( (-\infty, 1) \cup (6, \infty) \).