Answer
The solution is: $(-1,3)$
Work Step by Step
In order to solve the inequality
$ 1 \lt 2x+3 \lt 9$
we start by isolating (solving for) $x$.
First, we subtract $3$:
$1-3 \lt 2x+3-3 \lt 9-3$
$-2 \lt 2x \lt 6$
Next, we divide by $2$:
$-2\div2 \lt 2x\div \lt 6\div 2$
$-1 \lt x \lt 3$
The result can be written as:
$(-1,3)$
