Question

If-8<-2t +1 < -1, what is a possible integer value of 4t - 2?

Answer 1

`-8 < -2t+1 < -1\implies -8-1 < -2t+1-1 < -1-1 \\\\\\ -9 < -2t < -2\implies \stackrel{\textit{notice, division by -2}}{\cfrac{-9}{-2}\stackrel{\downarrow }{ > }\cfrac{-2t}{-2}\stackrel{\downarrow }{ > }\cfrac{-2}{-2}}\implies \cfrac{9}{2} > t > 1`

`4(1)/(2) > t > 1\implies \begin{cases} t < 4(1)/(2)\\\\ t > 1 \end{cases}\hspace{5em}\stackrel{\textit{valid integers for`