Question 147213


Let's solve the first inequality {{{2x-4<0}}}:



{{{2x-4<0}}} Start with the first inequality.



{{{2x<0+4}}} Add {{{4}}} to both sides.



{{{2x<4}}} Combine like terms on the right side.



{{{x<(4)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}. 



{{{x<2}}} Reduce.



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Now let's solve the second inequality {{{6-x<3}}}:



{{{6-x<3}}} Start with the second inequality.



{{{-x<3-6}}} Subtract {{{6}}} from both sides.



{{{-x<-3}}} Combine like terms on the right side.



{{{x>(-3)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>3}}} Reduce.



So our answer is {{{x<2}}} <font size="4"><b>or</b></font>  {{{x>3}}}




So the solution in interval notation is: <font size="8">(</font>*[Tex \LARGE \bf{-\infty,2}]<font size="8">)</font> *[Tex \LARGE \cup]<font size="8">(</font>*[Tex \LARGE \bf{3,\infty}]<font size="8">)</font>