Alternative Equation Formats

$${\displaystyle y=\{\begin{array}{cl}{x}_1& \text{if}{w}_1>pW\\ \frac{1}{2}(x_i+x_{i+1})& \text{if}\underset{j=1}{\overset{i}{\sum <!--\; \sum \; -->}}{w}_j=pW\\ x_{i+1}& \text{if}\underset{j=1}{\overset{i}{\sum <!--\; \sum \; -->}}{w}_j<pW<\underset{j=1}{\overset{i+1}{\sum <!--\; \sum \; -->}}{w}_j\end{array}}$$

$${\displaystyle y=\{\begin{array}{cl}{x}_1& \text{if}{w}_1>pW\\ \frac{1}{2}(x_i+x_{i+1})& \text{if}\underset{j=1}{\overset{i}{\sum <!--\; \sum \; -->}}{w}_j=pW\\ x_{i+1}& \text{if}\underset{j=1}{\overset{i}{\sum <!--\; \sum \; -->}}{w}_j<pW<\underset{j=1}{\overset{i+1}{\sum <!--\; \sum \; -->}}{w}_j\end{array}}$$

\[ y = \left\{ \begin{array}{cl} x_1 & \mbox{if} \ w_1 > pW \\ \frac{1}{2} ( x_ i + x_{i+1} ) & \mbox{if} \sum _{j=1}^{i} w_ j = pW \\ x_{i+1} & \mbox{if} \sum _{j=1}^{i} w_ j < pW < \sum _{j=1}^{i+1} w_ j \end{array} \right. \]