Find all $u$ such that neither $2u$ nor $-2u + 7$ is in the interval $(-\infty,1)$.
1 answer
We use casework. Firstly assume $2u > 1$. Then $u > \frac12$. Next assume $-2u + 7 > 1$. Then $-2u > -6$ and $u < 3$. Therefore $u \in \boxed{\left(\frac 12,3\right)}$.