Question 156129
{{{2(5y-6)>=3y+6}}} Start with the given inequality.



{{{10y-12>=3y+6}}} Distribute.



{{{10y>=3y+6+12}}} Add {{{12}}} to both sides.



{{{10y-3y>=6+12}}} Subtract {{{3y}}} from both sides.



{{{7y>=6+12}}} Combine like terms on the left side.



{{{7y>=18}}} Combine like terms on the right side.



{{{y>=(18)/(7)}}} Divide both sides by {{{7}}} to isolate {{{y}}}. 



----------------------------------------------------------------------


Answer:


So the answer is {{{y>=18/7}}} 



Which approximates to {{{y>=2.571}}} 




So the solution set is  *[Tex \LARGE \left\{y\|y \ge \frac{18}{7}\right\}]



Also, the answer in interval notation is <font size="8">[</font>*[Tex \LARGE \frac{18}{7},\infty]<font size="8">)</font>



Finally, here's the graph of the solution set


{{{drawing(500,80,-3, 28,-10, 10,
number_line( 500, -3, 28),

arrow(18/7,0,28,0),
arrow(18/7,0.30,28,0.30),
arrow(18/7,0.15,28,0.15),
arrow(18/7,-0.15,28,-0.15),
arrow(18/7,-0.30,28,-0.30),

circle(18/7,0,0.3),
circle(18/7,0,0.25),
circle(18/7,0,0.2),
circle(18/7,0,0.2-0.02)
)}}}


Note: the endpoint is an closed circle