Answer:
[tex]\huge\boxed{-11<t<3\Rightarrow t\in(-11,\ 3)}[/tex]
Step-by-step explanation:
[tex]3+|t+4|<10\qquad\text{subtract 3 from both sides}\\\\3-3+|t+4|<10-3\\\\|t+4|<7\iff t+4<7\ \wedge\ t+4>-7\qquad\text{subtract 4 from both sides}\\\\t+4-4<7-4\ \wedge\ t+4-4>-7-4\\\\t<3\ \wedge\ t>-11\Rightarrow-11<t<3\Rightarrow t\in(-11,\ 3)[/tex]
