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Sagot :
Answer: We have to solve the provided inequality:
[tex]\frac{3}{5}(x-12)>x-24\Rightarrow(1)[/tex]The detailed steps for the solution to inequality (1) are as follows:
[tex]\begin{gathered} \begin{equation*} \frac{3}{5}(x-12)>x-24 \end{equation*} \\ \\ \text{ Multiply out the 3/5 on the left:} \\ \\ \frac{3x}{5}-\frac{36}{5}>x-24 \\ \\ \text{ Add 24 on both sides:} \\ \\ \\ \\ \frac{3x}{5}-\frac{36}{5}-24\gt x \\ \\ \\ \\ \text{ Subtract \lparen3x/5\rparen on both sides:} \\ \\ \\ \frac{36}{5}-24\gt x-\frac{3x}{5} \\ \\ \\ \\ \text{ Final steps is the simplification:} \\ \\ \frac{36}{5}-\frac{(24\times5)}{5}\gt\frac{x}{5}-\frac{3x}{5} \\ \\ \\ \frac{36}{5}-\frac{(24\times5)}{5}\gt\frac{(x\times5)}{5}-\frac{3x}{5} \\ \\ \\ \\ \frac{36-120}{5}\gt\frac{(5x-3x}{5} \\ \\ \\ -\frac{84}{5}>\frac{2}{5}x \\ \\ \\ \text{ Multiply both sides by \lparen5/2\rparen:} \\ \\ \\ \frac{5}{2}\times-\frac{84}{5}\gt\frac{5}{2}\times\frac{2}{5}x\Rightarrow-42>x \\ \\ \\ x<-42 \end{gathered}[/tex]Therefore the answer is that x is less than -42.
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