Answer
$\left[ -\dfrac{4}{3},2 \right)$
Work Step by Step
Using the properties of inequalities, then,
\begin{array}{l}
-\dfrac{1}{2}\le \dfrac{3x-1}{10}\lt\dfrac{1}{2}\\\\
-5(1)\le 1(3x-1)\lt5(1)
\text{...multiply all sides by 10}\\
-5\le 3x-1\lt5\\
-5+1\le 3x-1+1\lt5+1\\
-4\le 3x\lt6\\\\
-\dfrac{4}{3}\le x\lt2
.\end{array}
Using the conjunction "OR", the solution set is the combined solution of both inequalities. Hence, in interval notation form, the solution is $
\left[ -\dfrac{4}{3},2 \right)
$.
