Answer
$-2\le x\le3$
Work Step by Step
Since $|x|\le a$ (where $a$ is a positive constant) implies $-a\le x\le a,$ the given inequality, $
|2x-1|\le5
,$ is equivalent to
\begin{align*}
-5\le &2x-1\le5
.\end{align*}
Using the properties of inequality, the inequality above is equivalent to
\begin{align*}\require{cancel}
-5+1\le &2x-1+1\le5+1
\\
-4\le &2x\le6
\\\\
-\dfrac{4}{2}\le &\dfrac{\cancel2x}{\cancel2}\le\dfrac{6}{2}
\\\\
-2\le &x\le3
.\end{align*}
Hence, the solution to the inequality $|2x-1|\le5$ is $-2\le x\le3$.
