Question 133579
I'll do the first two to get you started


# 1



{{{2(2x-3)<6}}} Start with the given inequality




{{{4x-6<6}}} Distribute



{{{4x<6+6}}}Add 6 to both sides



{{{4x<12}}} Combine like terms on the right side



{{{x<(12)/(4)}}} Divide both sides by 4 to isolate x 




{{{x<3}}} Divide


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Answer:

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



So the solution set in set-builder notation is *[Tex \LARGE \textrm{\left{x|x<3\right}}]





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# 2





{{{3(3+4x)-8>=109}}} Start with the given inequality




{{{9+12x-8>=109}}} Distribute



{{{12x+1>=109}}} Combine like terms on the left side



{{{12x>=109-1}}}Subtract 1 from both sides



{{{12x>=108}}} Combine like terms on the right side



{{{x>=(108)/(12)}}} Divide both sides by 12 to isolate x 




{{{x>=9}}} Divide


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Answer:

So our answer is {{{x>=9}}} 





So the solution set in set-builder notation is *[Tex \LARGE \textrm{\left{x|x\ge 9\right}}]