Question 178299
{{{(1/4)(8y+4)-34<-(1/3)(9y-6)}}} Start with the given inequality



{{{3(8y+4)-408<-4(9y-6)}}} Multiply EVERY term (that's not in a set of parenthesis) by the LCD 12 to clear the fractions.



{{{24y+12-408<-36y+24}}} Distribute.



{{{24y-396<-36y+24}}} Combine like terms on the left side.



{{{24y<-36y+24+396}}} Add {{{396}}} to both sides.



{{{24y+36y<24+396}}} Add {{{36y}}} to both sides.



{{{60y<24+396}}} Combine like terms on the left side.



{{{60y<420}}} Combine like terms on the right side.



{{{y<(420)/(60)}}} Divide both sides by {{{60}}} to isolate {{{y}}}. 



{{{y<7}}} Reduce.



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Answer:


So the answer is {{{y<7}}} 




So the answer in interval notation is *[Tex \LARGE \left(-\infty,7\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{y\|y<7\right\}]



Here's the graph of the solution set on the number line:


{{{drawing(500,80,-3, 17,-10, 10,
number_line( 500, -3, 17),


arrow(7,0,-3,0),
arrow(7,0.30,-3,0.30),
arrow(7,0.15,-3,0.15),
arrow(7,-0.15,-3,-0.15),
arrow(7,-0.30,-3,-0.30),




circle(7,0,0.3),
circle(7,0,0.3),
circle(7,0,0.3),
circle(7,0,0.3-0.02)
)}}}