Find the least integer value of $x$ for which $2|x| + 7 < 17$.
To simplify the inequality, I can subtract 7 from both sides, getting $2|x| < 10$. Then I can divide both sides by 2, getting $|x| < 5$. This means that $x$ can be any integer between -5 and 5, excluding the endpoints. The smallest such integer is -4, so that's my answer.

