Question 193076
Let's solve the first inequality {{{(2x-3)/6<=-9}}}:



{{{(2x-3)/6<=-9}}} Start with the first inequality.



{{{2x-3<=6(-9)}}} Multiply both sides by 6.



{{{2x-3<=-54}}} Multiply.



{{{2x<=-54+3}}} Add {{{3}}} to both sides.



{{{2x<=-51}}} Combine like terms on the right side.



{{{x<=(-51)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}. 



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Now let's solve the second inequality {{{(2x-3)/6>=1}}}:



{{{(2x-3)/6>=1}}} Start with the second inequality.



{{{2x-3>=6(1)}}} Multiply both sides by 6.



{{{2x-3>=6}}} Multiply.



{{{2x>=6+3}}} Add {{{3}}} to both sides.



{{{2x>=9}}} Combine like terms on the right side.



{{{x>=(9)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}. 



So our answer is {{{x<=-51/2}}} <font size="4"><b>or</b></font>  {{{x>=9/2}}}



Which in set-builder notation looks like *[Tex \LARGE \left\{x\|x\le-\frac{51}{2} \ \textrm{or} \ x\ge\frac{9}{2}\right\}]