# How do you solve 3abs(x-1)+2>=8?

Apr 10, 2015

If $3 \left\mid x - 1 \right\mid + 2 \ge 8$
then
$3 \left\mid x - 1 \right\mid \ge 6$
and
$\left\mid x - 1 \right\mid \ge 2$

If $\left(x - 1\right)$ is negative then
$1 - x \ge 2$
$- x \ge 1$
$x \le - 1$

If $\left(x - 1\right)$ is positive or zero
$x - 1 \ge 2$
$x \ge 3$

So $3 \left\mid x - 1 \right\mid + 2 \ge 8$
if
$x < - 1$
or
$x \ge 3$