Question 180820

{{{4-2x>11}}} Start with the given inequality.



{{{-2x>11-4}}} Subtract {{{4}}} from both sides.



{{{-2x>7}}} Combine like terms on the right side.



{{{x<(7)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<-7/2}}} Reduce.



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Answer:


So the answer is {{{x<-7/2}}} 



Which approximates to {{{x<-3.5}}} 




So the answer in interval notation is *[Tex \LARGE \left(-\infty,-\frac{7}{2}\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x<-\frac{7}{2}\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(-7/2,0,-17,0),
arrow(-7/2,0.30,-17,0.30),
arrow(-7/2,0.15,-17,0.15),
arrow(-7/2,-0.15,-17,-0.15),
arrow(-7/2,-0.30,-17,-0.30),




circle(-7/2,0,0.3),
circle(-7/2,0,0.3),
circle(-7/2,0,0.3),
circle(-7/2,0,0.3-0.02)
)}}} Graph of the solution set where the open circle denotes the excluded value.