Q.Solve $|2x + 3| \ge 7$ for real $x$, and represent the solution set on the number line.

The modulus $|x|$ measures a real number's distance from $0$ on the number line, and $|x-c|$ measures distance from the point $c$. Two equivalences, both provable by splitting into the cases $x\ge0$ and $x<0$, govern every modulus inequality: $|x|<a \iff -a<x<a$ (a single bounded interval, since being close to $0$ means lying between two symmetric bounds), and $|x|>a \iff x<-a$ or $x>a$ (two disjoint unbounded rays, since being *f …