Question 160058


Let's solve the first inequality {{{-2x<-8}}}:



{{{-2x<-8}}} Start with the first inequality.



{{{x>(-8)/(-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>4}}} Reduce.



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Now let's solve the second inequality {{{x-5<5}}}:



{{{x-5<5}}} Start with the second inequality.



{{{x<5+5}}} Add {{{5}}} to both sides.



{{{x<10}}} Combine like terms on the right side.



So our answer is {{{x>4}}} <font size="4"><b>and</b></font>  {{{x<10}}}



Which combines to the compound inequality {{{4<x<10}}}