Answer
The value of the expression $\left| 2x+1 \right|\le 1$ is $ x=\left[ -1,0 \right]$.
Work Step by Step
The provided function is a modulus function, so rewrite it as:
$2x+1\le 1$ And $-\left( 2x+1 \right)\le 1$
Then, solve the first inequality to get:
$\begin{align}
& 2x+1\le 1 \\
& 2x\le 0 \\
& x\le 0
\end{align}$
Again, solve the second inequality:
$\begin{align}
& -\left( 2x+1 \right)\le 1 \\
& -2x-1\le 1 \\
& -2x\le 2
\end{align}$
And simplify it further to get:
$\begin{align}
& 2x\ge -2 \\
& x\ge -1
\end{align}$
