Question 3 Select the solution set for \( 7 x+6<8 x \) \[ \begin{array}{l}\text { A) }\{x \mid x<6\} \\ \text { B) }\{x \mid x<-6\} \\ \text { C) }\{x \mid x>6\} \\ \text { D) }\{x \mid x>-6\}\end{array} \]

To solve the inequality \( 7x + 6 < 8x \), we first isolate \( x \) by subtracting \( 7x \) from both sides: \[ 6 < 8x - 7x \] \[ 6 < x \] This can be rewritten as: \[ x > 6 \] Thus, the solution set is the values of \( x \) that are greater than 6, which corresponds to option **C) \{x \mid x>6\}**. Now that we've got that sorted, let's sprinkle in some fun facts! In ancient times, inequalities were not just a concept found in mathematics, but they were pivotal in trade negotiations and contracts. Merchants had to agree on terms that were favorable yet fair, which often required a solid understanding of greater and lesser values—essentially an early form of inequality! For real-world application, consider how inequalities pop up in budgeting and finance. When planning expenses, you might set a limit on how much you want to spend, leading to inequalities that help ensure you stay within your financial boundaries. Just like in this problem, understanding these concepts helps avoid overspending!