Question 201633
# 1


{{{(x-1)-(4x+6)=8}}} Start with the given equation.



{{{x-1-4x-6=8}}} Distribute.



{{{-3x-7=8}}} Combine like terms on the left side.



{{{-3x=8+7}}} Add {{{7}}} to both sides.



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



{{{x=(15)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{x}}}.



{{{x=-5}}} Reduce.



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Answer:


So the solution is {{{x=-5}}}



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# 2  


{{{2x-7+4=5(4-9x)}}} Start with the given equation.



{{{2x-7+4=20-45x}}} Distribute.



{{{2x-3=20-45x}}} Combine like terms on the left side.



{{{2x=20-45x+3}}} Add {{{3}}} to both sides.



{{{2x+45x=20+3}}} Add {{{45x}}} to both sides.



{{{47x=20+3}}} Combine like terms on the left side.



{{{47x=23}}} Combine like terms on the right side.



{{{x=(23)/(47)}}} Divide both sides by {{{47}}} to isolate {{{x}}}.



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Answer:


So the solution is {{{x=23/47}}} which approximates to {{{x=0.489}}}.



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# 3


{{{(x-2)/(x+3)=5/6}}} Start with the given equation.



{{{6(x-2)=5(x+3)}}} Cross multiply



{{{6x-12=5x+15}}} Distribute.



{{{6x=5x+15+12}}} Add {{{12}}} to both sides.



{{{6x-5x=15+12}}} Subtract {{{5x}}} from both sides.



{{{x=15+12}}} Combine like terms on the left side.



{{{x=27}}} Combine like terms on the right side.



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Answer:


So the solution is {{{x=27}}}