Question

Solve.

3 + |t + 4| < 10

Answer 1

`\huge\boxed{-11<t<3\Rightarrow t\in(-11,\ 3)}`

Explanation:

`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)`

Answer 2

3 + |t + 4| < 10

Subtract 3

|t + 4| < 7

Because it is absolute value...

t + 4 < 7 AND t + 4 > -7

t < 3 AND t > -11

ANSWER:

t < 3 AND t > -11