Answer
$$2 \lt x \lt 11$$
Work Step by Step
We solve the inequalities using the rules of inequalities. These are the same as if there were an equal sign instead of an inequality symbol, but note that the inequality symbol must be flipped if we multiply or divide both sides by a negative. Doing this, we obtain:
$$ -1<10-x<8\\ -1<10-x\quad \mathrm{and}\quad \:10-x<8\\ x<11\quad \mathrm{and}\quad \:x>2\\ 2 \lt x \lt 11$$
