Answer
$\color{blue}{\left\{\dfrac{1-2\sqrt3}{3}, \dfrac{1+2\sqrt3}{3}\right\}}$
Work Step by Step
RECALL:
If $x^2=a$, then taking the square root of both sides gives $x = \pm \sqrt{a}$.
Take the square root of both sides of the given equation to obtain:
$\sqrt{(3x-1)^2}=\pm \sqrt{12}
\\3x-1 =\pm \sqrt{4(3)}
\\3x-1=\pm\sqrt{2^2(3)}
\\3x-1 =\pm 2\sqrt{3}$
Add $1$ to both sides:
$3x =1 \pm 2\sqrt{3}$
Divide $3$ to both sides:
$x=\dfrac{1\pm2\sqrt3}{3}$
Thus, the solution set is $\color{blue}{\left\{\dfrac{1-2\sqrt3}{3}, \dfrac{1+2\sqrt3}{3}\right\}}$.
