Hey , I have a quick question about a Homework in math I got confused on how to solve the listed to formula (x - 3)/(2) - 4 \ \textless \ (x)/(3)

Question

Hey , I have a quick question about a Homework in math I got confused on how to solve the listed to formula
`(x - 3)/(2) - 4 \ \textless \ (x)/(3)`

Answer 1

- The question would like us to solve the following

`(x-3)/(2)-4<(x)/(3)`

- The solution is outlined below:

`\begin{gathered} (x-3)/(2)-4<(x)/(3) \\ \\ Collect\text{ like terms:} \\ Add\text{ 4 to both sides and Subtract }(x)/(3)\text{ from both sides} \\ \\ (x-3)/(2)-(x)/(3)<4 \\ \\ We\text{ need the LCM of 2 and 3. } \\ The\text{ LCM is }2*3=6 \\ \\ Thus,\text{ multiply both sides by 6 in order to remove the denominator} \\ 2\frac{}{} \end{gathered}`
`\begin{gathered} 6\left((x-3)/(2)\right?-6\left((x)/(3)\right?<4*6 \\ \\ 3\left(x-3\right)-2x<24 \\ Expand\text{ the bracket} \\ 3x-9-2x<24 \\ x-9<24 \\ Add\text{ 9 to both sides} \\ x<33 \end{gathered}`

Final Answer

The answer is x < 33