Answer
Solution in interval notation:
$(-5,-2]$
See graph below.
Work Step by Step
We are asked to solve the inequality:
$-11\lt 2x -1 \le -5$
To obtain the solution, we need to isolate $x$.
We add $1$ to all sides:
$-11+1\lt 2x -1 +1 \le -5+1$
$-10\lt 2x \le -4$
Now, we divide by $2$:
$-10\div 2\lt 2x \div 2\le -4 \div 2$
$-5\lt x \le -2$
In interval notation, this can be written as:
$(-5,-2]$
See the graph of the inequality below.
