1. The solution of \( \frac{x}{2}-x=\frac{3 x}{8}-11 \) is: \( \begin{array}{llll}\text { a. } \frac{7}{2} & \text { b. } \frac{7}{11} & \text { c. } \frac{88}{7} & \text { d. }-\frac{11}{7}\end{array} \)

To solve the equation \( \frac{x}{2} - x = \frac{3x}{8} - 11 \), we first simplify the left side: \[ \frac{x}{2} - x = \frac{x}{2} - \frac{2x}{2} = -\frac{x}{2}. \] Now the equation becomes: \[ -\frac{x}{2} = \frac{3x}{8} - 11. \] Next, we can multiply the entire equation by 8 to eliminate the fractions: \[ -4x = 3x - 88. \] Now, rearranging gives us: \[ -4x - 3x = -88 \Rightarrow -7x = -88 \Rightarrow x = \frac{88}{7}. \] Thus, the answer is \( c. \frac{88}{7} \). Now for some helpful insights: The history of algebra dates back thousands of years, with roots in ancient Babylonian mathematics. The development of algebraic notation, like using letters for variables, evolved during the Middle Ages, enabling more complex equations to be solved systematically. In the real world, understanding equations helps us in various fields such as engineering, finance, and technology. For instance, engineers use algebra to calculate loads and stresses in structures, ensuring safety and reliability in buildings and bridges.