Question 641710
{{{2(x+3)/5>2x-6}}} Start with the given inequality.



{{{2(x+3)>5(2x-6)}}} Multiply both sides by 5.



{{{2x+6>10x-30}}} Distribute.



{{{2x>10x-30-6}}} Subtract {{{6}}} from both sides.



{{{2x-10x>-30-6}}} Subtract {{{10x}}} from both sides.



{{{-8x>-30-6}}} Combine like terms on the left side.



{{{-8x>-36}}} Combine like terms on the right side.



{{{x<(-36)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<9/2}}} Reduce.



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Answer:


So the solution is {{{x<9/2}}}