How do you solve 1<3x-5<=4?

$2 < x \le 3$.
$3 x - 5 \le 4$. So, $3 x \le 9 \mathmr{and} x \le 3$.
$3 x - 5 > 1$. So, $3 x > 6 \mathmr{and} x > 2$.combine.
$2 < x \le 3$.