I need help understanding this proof. I want to know why everything is done. Walk me through this please and help me understand.

Why is b $=(1-$a $/4)$ specifically. Why is it over $4?$ Where is that thinking coming from $.$ Teach me the way of thinking used for this question and explain it to me$.$

Prove $$a in R$,$ if a then $$b in $(0,\backslash$infty $),$ a $+2$b $<mtext\; id="EditorElement\_515843"></mtext><mn\; id="EditorElement\_515844">1</mn>$