Question 117961
Let's solve the first inequality



{{{x-2>2x+1}}} Start with the first inequality




{{{x>2x+1+2}}}Add 2 to both sides



{{{x-2x>1+2}}} Subtract 2x from both sides



{{{-x>1+2}}} Combine like terms on the left side



{{{-x>3}}} Combine like terms on the right side



{{{x<(3)/(-1)}}} Divide both sides by -1 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{x<-3}}} Divide


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Answer:

So our first answer is {{{x<-3}}} 



Now let's solve the second inequality




{{{10>-2x+2}}} Start with the second inequality




{{{0>-2x+2-10}}}Subtract 10 from both sides



{{{+2x>2-10}}} Add 2x to both sides



{{{2x+0>-8}}} Combine like terms on the right side



{{{x>(-8)/(2)}}} Divide both sides by 2 to isolate x 




{{{x>-4}}} Divide


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Answer:

So our answer is {{{x>-4}}} 




So our solution is {{{x<-3}}} or {{{x>-4}}}