Question 317771
{{{-(2/3)z+9>=(2/3)z+1}}} Start with the given inequality.



{{{3(-(2/cross(3))z+9)>=3((2/cross(3))z+1)}}} Multiply both sides by the LCD {{{3}}} to clear any fractions.



{{{-2z+27>=2z+3}}} Distribute and multiply.



{{{-2z>=2z+3-27}}} Subtract {{{27}}} from both sides.



{{{-2z-2z>=3-27}}} Subtract {{{2z}}} from both sides.



{{{-4z>=3-27}}} Combine like terms on the left side.



{{{-4z>=-24}}} Combine like terms on the right side.



{{{z<=(-24)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{z}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{z<=6}}} Reduce.



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Answer:


So the solution is {{{z<=6}}}