Question 632456


{{{-2(10x-9)-17x<12(6-x)}}} Start with the given inequality.



{{{-20x+18-17x<72-12x}}} Distribute.



{{{-37x+18<72-12x}}} Combine like terms on the left side.



{{{-37x<72-12x-18}}} Subtract {{{18}}} from both sides.



{{{-37x+12x<72-18}}} Add {{{12x}}} to both sides.



{{{-25x<72-18}}} Combine like terms on the left side.



{{{-25x<54}}} Combine like terms on the right side.



{{{x>(54)/(-25)}}} Divide both sides by {{{-25}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>-54/25}}} Reduce.



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Answer:


So the solution is {{{x>-54/25}}} 



So the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x>-\frac{54}{25}\right\}]


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