Answer
Interval: $(-\infty,\ \infty)$
Work Step by Step
$7|x+2|+5\gt4$
$7|x+2|\gt4-5$
$ 7|x+2|\gt-1$
$|x+2|\gt-\frac{1}{7}$
The absolute value is always positive and thus is always greater than $-\frac{1}{7}$. So this inequality holds true for all real numbers.
Interval: $(-\infty,\ \infty)$
