Answer
$t\leq -\frac{2}{3}$ or $t\geq 3$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |6t-7|-8\geq 3$
Add $8$ to each side.
$\Rightarrow |6t-7|-8+8\geq 3+8$
Simplify.
$\Rightarrow |6t-7|\geq 11$
Write a compound inequality.
$\Rightarrow 6t-7\leq -11$ or $6t-7\geq 11$
Add $7$ to each side.
$\Rightarrow 6t-7+7\leq -11+7$ or $6t-7+7\geq 11+7$
Simplify.
$\Rightarrow 6t\leq -4$ or $6t\geq 18$
Divide each side by $6$.
$\Rightarrow \frac{6t}{6}\leq \frac{-4}{6}$ or $\frac{6t}{6}\geq \frac{18}{6}$
Simplify.
$\Rightarrow t\leq -\frac{2}{3}$ or $t\geq 3$
Hence, the solution is $t\leq -\frac{2}{3}$ or $t\geq 3$.
