Answer
$t\le-1 \text{ or } t\ge1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Solve the given inequality, $
|t|\ge1
,$ using the definition of a greater than absolute value inequality. Then graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
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 given inequality is equivalent to \begin{array}{l}\require{cancel} t\ge1 \\\\\text{OR}\\\\ t\le-1 .\end{array}
Hence, the solution set is $
t\le-1 \text{ or } t\ge1
.$
