Solve the compound inequality. Express the answer in interval notation.
(A) $-3x+1\le 4$ and

• A. $[1,3)$
• B. $[4,3)$
• C. $[-1,5)$
• D. $(1,\frac{5}{3}]$

Answer: (C)

Verified step by step guidance

1. Start by solving each inequality separately. For the first inequality, \(-3x + 1 \leq 4\), isolate the variable term by subtracting 1 from both sides to get \(-3x \leq 3\).
2. Next, divide both sides of the inequality \(-3x \leq 3\) by \(-3\). Remember, when dividing by a negative number, the inequality sign reverses, so you get \(x \geq -1\).
3. Now, solve the second inequality \(x - 2 < 3\) by adding 2 to both sides, resulting in \(x < 5\).
4. Combine the two solutions to form the compound inequality: \(x \geq -1\) and \(x < 5\). This means \(x\) is greater than or equal to \(-1\) and less than \$5$ simultaneously.
5. Express the solution in interval notation. Since \(x\) is greater than or equal to \(-1\) (closed bracket) and less than \$5\( (open bracket), the interval notation is \)\left[-1, 5\right)$.