Answer
Solution set = $\displaystyle \{-\frac{1}{2},-\frac{9}{2}\}$
Work Step by Step
Use properties from the table 'Absolute Values and Intervals",
Here: property 5: $|x|=a \Leftrightarrow x=\pm a,\ \quad $(for any positive number a)
Thus:
$2t+5=\pm 4\qquad $... add $-5$
$2t=-5\pm 4\qquad $... divide with 2,
$t=\displaystyle \frac{-5\pm 4}{2}$
$\displaystyle \frac{-5+4}{2}=-\frac{1}{2}$
$\displaystyle \frac{-5-4}{2}=-\frac{9}{2}$
Solution set = $\displaystyle \{-\frac{1}{2},-\frac{9}{2}\}$
