The inequality can be solved as follows
[tex]\begin{gathered} 18(\frac{1}{3}x+6)>3(2x-6) \\ \text{divide by 3} \\ 6(\frac{1}{3}x+6)>2x-6 \\ \text{Multiply 6 with terms inside brackets} \\ \frac{6\ast x}{3}+6\ast6>2x-6 \\ 2x+36>2x-6 \\ \text{Move 36 to right side} \\ 2x>2x-6-36 \\ \end{gathered}[/tex][tex]\begin{gathered} 2x>2x-42 \\ \text{Move 2x to the left side of inequality} \\ 2x-2x>-42 \\ 0>-42 \end{gathered}[/tex]
0>-42 is a true statement. Thus, the inequality have an infinite number of solutions.
