Question 134097
# 1




{{{14x-8<-50}}} Start with the given inequality




{{{14x+cross(-8+8)<-50+8}}} Add 8 to both sides



{{{14x<-42}}} Combine like terms



{{{(1/cross(14))cross(14)x<(1/14)(-42)}}} Multiply both sides by {{{1/14}}} to isolate x 




{{{x<-3}}} Multiply and simplify


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Answer:

So our answer is {{{x<-3}}} 



So the answer in set-builder notation is *[Tex \LARGE \textrm{\left{x|x<-3\right}}]




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# 2




{{{x/6-1<1/5}}} Start with the given inequality




{{{(30)(x/cross(6)-1)<(30)(1/cross(5))}}} Multiply both sides by the LCM of 30. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)




{{{5x-30<6}}} Distribute and multiply the LCM to each side




{{{5x+cross(-30+30)<6+30}}}Add 30 to both sides



{{{5x<36}}} Combine like terms



{{{(1/cross(5))cross(5)x<(1/5)36}}} Multiply  both sides by {{{1/5}}} to isolate x 




{{{x<36/5}}} Multiply


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Answer:

So our answer is {{{x<36/5}}}  (which is approximately {{{x<7.2}}} in decimal form)



So the answer in set-builder notation is *[Tex \LARGE \textrm{\left{x|x<\frac{36}{5}\right}}] or *[Tex \LARGE \textrm{\left{x|x<7.2\right}}] (which is in decimal form)