Discussion
The solution set of the inequality \(6(2x + 3) + x \gt 53 - 2x\) is
Answer: A
The solution set is \(\left(\frac{7}{3}, \infty\right)\).
\[ \begin{aligned} 6(2x + 3) + x &\gt 53 - 2x \\ 12x + 18 + x &\gt 53 - 2x \\ 15x &\gt 35 \\ x &\gt \tfrac{7}{3} \end{aligned} \]
Dividing by the positive number 15 does not reverse the inequality, so every \(x\) greater than \(\frac{7}{3}\) works. The set \(\left(-\infty, \frac{7}{3}\right)\) reverses the sign, and the bounded intervals add a limit the inequality does not have.
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