Solve the inequalities $3x-1<2x+3\le7+5x$.

1. Split the compound inequality into two inequalities.

$3x-1<2x+3\le 7+5x$

This means

$3x-1<2x+3$ and $2x+3\le 7+5x$.

2. Solve the left inequality.

$3x-1<2x+3$

$3x-2x<3+1$

$x<4$

3. Solve the right inequality and combine both results.

$2x+3\le 7+5x$

$2x-5x\le 7-3$

$-3x\le 4$

Dividing by $-3$ reverses the inequality sign:

$x\ge -\dfrac{4}{3}$

Combining with $x<4$,

$-\dfrac{4}{3}\le x<4$.