Answer
$\left\{x\ |\ 0.5 \leq x \lt 1.25 \right\}$ or $\left[0.5, \ 1.25 \right)$
Work Step by Step
$\displaystyle \frac{1}{2} \leq \frac{x+1}{3} \lt \frac{3}{4} \qquad$... multiply with $12$, the LCD
$6 \leq 4(x+1) \lt 9$
$ 6 \leq 4x+4 \lt 9 \qquad$ ... add $-4$
$ 2 \leq 4x \lt 5 \qquad$... multiply with $\displaystyle \frac{1}{4}$
$\displaystyle \frac{1}{2} \leq x \lt \frac{5}{4} $
Solution set: $\left\{x\ |\ 0.5 \leq x \lt 1.25 \right\}$ or $\left[0.5, \ 1.25 \right)$
