Question 242466
#1



{{{6(2x+8)-5(x-7)=5x+91+x}}} Start with the given equation.



{{{12x+48-5x+35=5x+91+x}}} Distribute.



{{{7x+83=5x+91+x}}} Combine like terms on the left side.



{{{7x+83=6x+91}}} Combine like terms on the right side.



{{{7x=6x+91-83}}} Subtract {{{83}}} from both sides.



{{{7x-6x=91-83}}} Subtract {{{6x}}} from both sides.



{{{x=91-83}}} Combine like terms on the left side.



{{{x=8}}} Combine like terms on the right side.



----------------------------------------------------------------------


Answer:


So the solution is {{{x=8}}} 


<hr>


# 2



{{{3(3x+1)=5-5(3x-3)}}} Start with the given equation.



{{{9x+3=5-15x+15}}} Distribute.



{{{9x+3=-15x+20}}} Combine like terms on the right side.



{{{9x=-15x+20-3}}} Subtract {{{3}}} from both sides.



{{{9x+15x=20-3}}} Add {{{15x}}} to both sides.



{{{24x=20-3}}} Combine like terms on the left side.



{{{24x=17}}} Combine like terms on the right side.



{{{x=(17)/(24)}}} Divide both sides by {{{24}}} to isolate {{{x}}}.



----------------------------------------------------------------------


Answer:


So the solution is {{{x=17/24}}} which approximates to {{{x=0.708}}}. 


<hr>


# 3



{{{2-8(x+3)<-38-3(x+8)+3x}}} Start with the given inequality.



{{{2-8x-24<-38-3x-24+3x}}} Distribute.



{{{-8x-22<-38-3x-24+3x}}} Combine like terms on the left side.



{{{-8x-22<-62}}} Combine like terms on the right side.



{{{-8x<-62+22}}} Add {{{22}}} to both sides.



{{{-8x<-40}}} Combine like terms on the right side.



{{{x>(-40)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>5}}} Reduce.



----------------------------------------------------------------------


Answer:


So the solution is {{{x>5}}}