Question 143890
{{{(9/10)(3+2x)+2>=23}}}


Solve this just the same way you would solve it if it were an equation instead of an inequality, except that if you have to multiply or divide by a negative number, you must reverse the sense of the inequality.


{{{(9/10)(3+2x)>=21}}}
{{{9(3+2x)>=210}}}
{{{27+18x>=210}}}
{{{18x>=183}}}
{{{x>=61/6}}}


Check:
{{{(9/10)(3+2(61/6))+2>=23}}}
{{{(9/10)(18/6+122/6)+2>=23}}}
{{{(9/10)(140/6)+2>=23}}}
{{{(1260/60)+2>=23}}}
{{{(1380/60)=23}}}, so the equals part is ok.


Since {{{61/6}}} is a little bigger than 10, pick a larger number, say {{{27/2}}}.
{{{(9/10)(3+2(27/2)))+2>=23}}}
{{{(9/10)(30)+2>=23}}}
{{{27+2=29>23}}},  so the greater than part works.


Now pick a smaller number, say {{{17/2}}}
{{{(9/10)(3+2(17/2)))+2>=23}}}
{{{(9/10)(20)+2>=23}}}
{{{18+2=20<23}}},  so a smaller number makes the relationship fail.  Answer checks.