# How do you solve and write the following in interval notation: |x + 7| ≥ 2 ?

Jul 10, 2016

x in ]-oo,-9] uu [-5,+oo[

#### Explanation:

Since $| f \left(x\right) | \ge k$ is equivalent to:

$f \left(x\right) \le - k \mathmr{and} f \left(x\right) \ge k$,

in this case you can solve:

$x + 7 \le - 2 \mathmr{and} x + 7 \ge 2$

$x \le - 2 - 7 \mathmr{and} x \ge 2 - 7$

$x \le - 9 \mathmr{and} x \ge - 5$

or x in ]-oo,-9] uu [-5,+oo[