Question 634509
Note: it should be  >= and not =>, but that's ok




{{{x-9>=7(x+2)}}} Start with the given inequality.



{{{x-9>=7x+14}}} Distribute.



{{{x>=7x+14+9}}} Add {{{9}}} to both sides.



{{{x-7x>=14+9}}} Subtract {{{7x}}} from both sides.



{{{-6x>=14+9}}} Combine like terms on the left side.



{{{-6x>=23}}} Combine like terms on the right side.



{{{x<=(23)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<=-23/6}}} Reduce.



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Answer:


So the solution is {{{x<=-23/6}}} 



The answer in set-builder notation is  *[Tex \LARGE \left\{x\|x\le-\frac{23}{6}\right\}]