Precalculus: Mathematics for Calculus, 7th Edition

$(-\infty, \infty)$
Using the properties of inequality, the given expression, $7|x+2|+5\gt4 ,$ is equivalent to \begin{array}{l}\require{cancel} 7|x+2|\gt4-5 \\\\ 7|x+2|\gt-1 \\\\ |x+2|\gt-\dfrac{1}{7} .\end{array} The left side of the inequality is always a nonnegative number. This is always greater than the negative value at the right. Hence, the solution set is $(-\infty, \infty) .$