Prove that for any real numbers $a$ and $\delta\gt 0$ that the interval $(a-\delta,a+\delta)$ contains the closed interval $[a-\delta/2,a+\delta/2]$.

Problem: 

Prove that for any real numbers $a$ and $\delta\gt 0$ that the interval $(a-\delta,a+\delta)$ contains the closed interval $[a-\delta/2,a+\delta/2]$.

Answer: 

It is true that for any real numbers $a$ and $\delta\gt 0$ that the interval $(a-\delta,a+\delta)$ contains the closed interval $[a-\delta/2,a+\delta/2]$.