So I was doing practice on khan academy I came across this question. "If -20 < 8x+10 < −8, what is the possible range of values of 4x+5?" I wasn't able to solve it. but when I when I saw the explanation I still wasn't able to understand it. here is the past of the explanation that strikes me. it say " if we examine the structure of the inequality we will see that : 4x+5 = 8x+10/2 . can someone explain how to solve this and how they got 4x+5 = 8x=10/2 and why ?
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I assume you actually meant $4x+5 = (8x+10)/2$ which is true, noting that $(8x+10)/2 = \frac{8x}{2}+\frac{10}{2} = 4x+5$. Now, given the inequality $-20<8x+10<-8$, then, dividing the whole inequality by $2$ and given that $2>0$, we have that $\frac{-20}{2}<\frac{8x+10}{2}<\frac{-8}{2}$, which implies that $-10<4x+5<-4$.
