Solve

1. Isolate the term containing $x$ and solve for $x$.

$3-4x=21$
$-4x=21-3$
$-4x=18$
$x=\frac{18}{-4}=-\frac{9}{2}$

1. Separate the compound inequality into two simple inequalities.

$2x<3x+1\le13$

This means

$2x<3x+1$ and $3x+1\le13$.

2. Solve the lower-bound inequality.

$2x<3x+1$

$2x-3x<1$

$-x<1$

$x>-1$

3. Solve the upper-bound inequality and combine the results.

$3x+1\le13$

$3x\le12$

$x\le4$

Combining with $x>-1$ gives

$-1<x\le4$.