Answer
$(-\infty,-1) \cup (4, \infty)$
Work Step by Step
Given: $|2x-3| +1\gt 6$
or, $|2x-3| \gt 6-1$
or,$2x-3 \gt 5$
or, $x \gt 4$
Now, $|2x-3| \gt 6-1$
or,$2x-3 \lt -5 \implies 2x \lt -2$
or, $x \lt -1$
Hence, $(-\infty,-1) \cup (4, \infty)$
