Answer
$a=-5$ and $b=7$
Work Step by Step
We are given:
$-3\lt x\lt 3$
We multiply by $-2$:
$-2*-3\gt -2*x\gt -2*3$
$6\gt -2x\gt -6$
We add $1$:
$6+1\gt -2x+1\gt -6+1$
$7\gt -2x+1\gt -5$
$-5\lt 1-2x\lt 7$
Therefore:
$a=-5$ and $b=7$