Answer
$(-\infty,4)$.
The graph of the solution set is shown below.
Work Step by Step
The given compound inequality is
$2x-3\lt5$ or $3x-6\leq4$.
Solve each inequality separately.
First $=2x-3\lt5$.
Add $3$ to both sides.
$=2x-3+3\lt5+3$
Simplify.
$=2x\lt8$
Divide both sides by $2$.
$=\frac{2x}{2}\lt\frac{8}{2}$
Simplify.
$=x\lt4$
Second $=3x-6\leq4$.
Add $6$ to both sides.
$=3x-6+6\leq4+6$
Simplify.
$=3x\leq10$
Divide both sides by $3$.
$=\frac{3x}{3}\leq\frac{10}{3}$
Simplify.
$=x\leq\frac{10}{3}$
First graph then take the union of the two inequality.
We can write the compound inequality.
$x\lt4$ as $(-\infty,4)$ and $x\leq\frac{10}{3}$ as $(-\infty,\frac{10}{3}]$
The union is
$(-\infty,4)\cup(-\infty,\frac{10}{3}]=(-\infty,4)$.
The combined graph is shown in the image file.
