Solve the compound inequality. Express the answer in interval notation.
(A) $- 3 x + 1 \leq 4$ and $x minus 2 is less than 3$

$\left\lbrack1,3\right)$

$\left\lbrack4,3\right)$

$\left\lbrack-1,5\right)$

$\left(1,\frac53\right\rbrack$

Verified step by step guidance

Start by writing down the two inequalities separately: $-3x + 1 \leq 4$ and $x - 2 < 3$.

Solve the first inequality for $x$: subtract 1 from both sides to isolate the term with $x$, giving $-3x \leq 3$.

Next, divide both sides of the inequality by $-3$. Remember, dividing by a negative number reverses the inequality sign, so you get $x \geq -1$.

Now solve the second inequality for $x$: add 2 to both sides to isolate $x$, resulting in $x < 5$.

Combine the two solutions to form the compound inequality: $x \geq -1$ and $x < 5$. Express this solution in interval notation as $\left[-1, 5\right)$.

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Solve the compound inequality. Express the answer in interval notation.(A) −3x+1≤4-3x+1\le4 and x−2<3x-2<3

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Solve the compound inequality. Express the answer in interval notation.
(A) $- 3 x + 1 \leq 4$ and $x minus 2 is less than 3$