Question 395802

{{{3(x-2)>4(2x+11)}}} Start with the given inequality.



{{{3x-6>8x+44}}} Distribute.



{{{3x>8x+44+6}}} Add {{{6}}} to both sides.



{{{3x-8x>44+6}}} Subtract {{{8x}}} from both sides.



{{{-5x>44+6}}} Combine like terms on the left side.



{{{-5x>50}}} Combine like terms on the right side.



{{{x<(50)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<-10}}} Reduce.



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Answer:


So the solution is {{{x<-10}}} 


So the answer in interval notation is *[Tex \LARGE \left(-\infty,-10\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x<-10\right\}]



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


{{{drawing(500,80,-20, 0,-10, 10,
number_line( 500, -20, 0),


arrow(-10,0,-20,0),
arrow(-10,0.30,-20,0.30),
arrow(-10,0.15,-20,0.15),
arrow(-10,-0.15,-20,-0.15),
arrow(-10,-0.30,-20,-0.30),




circle(-10,0,0.3),
circle(-10,0,0.3),
circle(-10,0,0.3),
circle(-10,0,0.3-0.02)
)}}}


Note: there is an open circle at the endpoint.



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Jim