Answer
$\{-1,\frac{3}{2}\}$
Work Step by Step
Recall that $|a|=b \implies a=b$ or $a=-b$.
Thus, using the rule above yields:
$1-4t=5\quad$ or $\quad 1-4t=-5$
Subtract $1$ from both sides of each equation.
$1-4t-1=5-1\quad$ or $\quad1-4t-1=-5-1$
Simplify.
$-4t=4\quad$ or $\quad-4t=-6$
Divide both sides of both equations by $-4$.
$\dfrac{-4t}{-4}=\dfrac{4}{-4}\quad$ or $\quad\dfrac{-4t}{-4}=\dfrac{-6}{-4}$
Simplify.
$t=-1\quad$ or $\quad t=\frac{3}{2}$
Hence, the solution set of the given equation is $\{-1,\frac{3}{2}\}$.
