Answer
$t\lt-3 \text{ or } t\gt3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|4t|\gt12
,$ use the definition of greater than (greater than or equal to) absolute value inequality and solve each resulting inequality.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
4t\gt12
\\\\\text{OR}\\\\
4t\lt-12
.\end{array}
Solving each inequality results to
\begin{array}{l}\require{cancel}
4t\gt12
\\\\
t\gt\dfrac{12}{4}
\\\\
t\gt3
\\\\\text{OR}\\\\
4t\lt-12
\\\\
t\lt-\dfrac{12}{4}
\\\\
t\lt-3
.\end{array}
Hence, the solution set is $
t\lt-3 \text{ or } t\gt3
.$
