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

• A. $\left\lbrack1,3\right)$
• B. $\left\lbrack4,3\right)$
• C. $\left\lbrack-1,5\right)$
• D. $\left(1,\frac53\right\rbrack$

Answer: (C)

Verified step by step guidance

1. Start by writing down the two inequalities separately: \(-3x + 1 \leq 4\) and \(x - 2 < 3\).
2. Solve the first inequality for \(x\): subtract 1 from both sides to isolate the term with \(x\), giving \(-3x \leq 3\).
3. Next, divide both sides of the inequality by \(-3\). Remember, dividing by a negative number reverses the inequality sign, so you get \(x \geq -1\).
4. Now solve the second inequality for \(x\): add 2 to both sides to isolate \(x\), resulting in \(x < 5\).
5. Combine the two solutions to form the compound inequality: \(x \geq -1\) and \(x < 5\). Express this solution in interval notation as \(\left[-1, 5\right)\).