Question

Solve the inequality). 3/5(x-12)>x-24

Answer 1

Answer: We have to solve the provided inequality:

`(3)/(5)(x-12)>x-24\Rightarrow(1)`

The detailed steps for the solution to inequality (1) are as follows:

`\begin{gathered} \begin{equation*} (3)/(5)(x-12)>x-24 \end{equation*} \\ \\ \text{ Multiply out the 3/5 on the left:} \\ \\ (3x)/(5)-(36)/(5)>x-24 \\ \\ \text{ Add 24 on both sides:} \\ \\ \\ \\ (3x)/(5)-(36)/(5)-24\gt x \\ \\ \\ \\ \text{ Subtract \lparen3x/5\rparen on both sides:} \\ \\ \\ (36)/(5)-24\gt x-(3x)/(5) \\ \\ \\ \\ \text{ Final steps is the simplification:} \\ \\ (36)/(5)-((24*5))/(5)\gt(x)/(5)-(3x)/(5) \\ \\ \\ (36)/(5)-((24*5))/(5)\gt((x*5))/(5)-(3x)/(5) \\ \\ \\ \\ (36-120)/(5)\gt((5x-3x)/(5) \\ \\ \\ -(84)/(5)>(2)/(5)x \\ \\ \\ \text{ Multiply both sides by \lparen5/2\rparen:} \\ \\ \\ (5)/(2)*-(84)/(5)\gt(5)/(2)*(2)/(5)x\Rightarrow-42>x \\ \\ \\ x<-42 \end{gathered}`

Therefore the answer is that x is less than -42.