Answer
Interval Notation: $(-∞,\frac{-11}{3})∪(-3,∞)$
Graph:
Work Step by Step
$|10+3x|+1 \gt 2$
By adding $-1$ to both sides of the inequality, isolate the absolute value expression.
$|10+3x|+1-1 \gt 2-1$
$|10+3x| \gt 1$
Using absolute value inequality property, it is equivalent to
$10+3x \lt -1$ or $ 10+3x \gt 1$
Add $-10$ to both sides of the inequalities,
$10+3x-10 \lt -1-10 $ or $ 10+3x-10 \gt 1-10$
$3x \lt -11 $ or $ 3x \gt -9$
Divide both sides of the inequalities by $3$
$x \lt \frac{-11}{3} $ or $ x \gt \frac{-9}{3}$
$x \lt \frac{-11}{3} $ or $ x \gt -3$
Interval Notation: $(-∞,\frac{-11}{3})∪(-3,∞)$