Question 337569

{{{3x+4<4(5x+4)-6}}} Start with the given inequality.



{{{3x+4<20x+16-6}}} Distribute.



{{{3x+4<20x+10}}} Combine like terms on the right side.



{{{3x<20x+10-4}}} Subtract {{{4}}} from both sides.



{{{3x-20x<10-4}}} Subtract {{{20x}}} from both sides.



{{{-17x<10-4}}} Combine like terms on the left side.



{{{-17x<6}}} Combine like terms on the right side.



{{{x>(6)/(-17)}}} Divide both sides by {{{-17}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>-6/17}}} Reduce.



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Answer:


So the solution is {{{x>-6/17}}} 



So the answer in interval notation is *[Tex \LARGE \left(-\frac{6}{17},\infty\right)]



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