For a real number \(x\), we call \(|x|\) its absolute value. It is defined as whichever is larger: \(x\) or \(-x\). For example, \(|-2|=2\) and \(|3|=3\).
One of the most important inequalities involving absolute values is the triangle inequality, which states that \[|a+b| \le |a| + |b|.\]
Show that this inequality is true.