Question 171396


{{{(1/2)x+3<2x-6}}} Start with the given inequality.



{{{2((1/cross(2))x+3)<2(2x-6)}}} Multiply both sides by the LCD {{{2}}} to clear any fractions.



{{{x+6<4x-12}}} Distribute and multiply.



{{{x<4x-12-6}}} Subtract {{{6}}} from both sides.



{{{x-4x<-12-6}}} Subtract {{{4x}}} from both sides.



{{{-3x<-12-6}}} Combine like terms on the left side.



{{{-3x<-18}}} Combine like terms on the right side.



{{{x>(-18)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>6}}} Reduce.



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Answer:


So the answer is {{{x>6}}}



So this means that  {{{(1/2)x+3<2x-6}}} is equivalent to {{{x>6}}}