#### Answer

$a$ $\leq$ $0$

#### Work Step by Step

$|2a-1|$ $\geq$ $2a+1$
Rewrite as a compound inequality:
$2a-1$ $\geq$ $2a+1$
or
$2a-1$ $\leq$ $-2a-1$.
Work through the first equation in the compound inequality by subtracting $2a$ from both sides:
$2a-1$ $\geq$ $2a+1$
$-1$ $\geq$ $1$.
Use the second equation since the first has no solution.
Work through the second equation by adding $2a$ and $1$ to both sides:
$2a-1$ $\leq$ $-2a-1$
$4a$ $\leq$ $0$.
Now divide by $4$
$a$ $\leq$ $0$.