## Precalculus (6th Edition) Blitzer

The value of the expression $\left| 2x+1 \right|\le 1$ is $x=\left[ -1,0 \right]$.
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}