Question 224971

{{{35-(4x+5)<2(x+2)+x}}} Start with the given inequality.



{{{35-4x-5<2x+4+x}}} Distribute.



{{{-4x+30<2x+4+x}}} Combine like terms on the left side.



{{{-4x+30<3x+4}}} Combine like terms on the right side.



{{{-4x<3x+4-30}}} Subtract {{{30}}} from both sides.



{{{-4x-3x<4-30}}} Subtract {{{3x}}} from both sides.



{{{-7x<4-30}}} Combine like terms on the left side.



{{{-7x<-26}}} Combine like terms on the right side.



{{{x>(-26)/(-7)}}} Divide both sides by {{{-7}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>26/7}}} Reduce.



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Answer:


So the solution is {{{x>26/7}}} 



Which approximates to {{{x>3.714}}} 



So the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x>\frac{26}{7}\right\}]