Question 369979
{{{5x+3<3x-11}}} Start with the given inequality.



{{{5x<3x-11-3}}} Subtract {{{3}}} from both sides.



{{{5x-3x<-11-3}}} Subtract {{{3x}}} from both sides.



{{{2x<-11-3}}} Combine like terms on the left side.



{{{2x<-14}}} Combine like terms on the right side.



{{{x<(-14)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}. 



{{{x<-7}}} Reduce.



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Answer:


So the solution is {{{x<-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\{x\|x<-7\right\}]



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


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


arrow(-7,0,-17,0),
arrow(-7,0.30,-17,0.30),
arrow(-7,0.15,-17,0.15),
arrow(-7,-0.15,-17,-0.15),
arrow(-7,-0.30,-17,-0.30),




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


Note: there's an open circle at {{{x=-7}}}



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Jim