I have encountered this inequality in Spivak's Calculus (first chapter exercises), which I'm not sure how to solve.
$$ 3^x + x < 4 $$
I might be wrong but my gut feeling says the inequality holds for all $x$ between $(-\infty, 1)$ but I cannot prove it.
As I read, there seems to be no standard scheme for solving this type of inequalities/equations. How do You then usually proceed when dealing with one like the above? Thanks.