Question

Resolução das equações:

7y-23=4(y+1)
4(5y+y)=210
3(6+3y)+2=2(y-9)-1
9y-5+4y=7y+2y+3

Answer 1

$7y-23=4(y+1)~~(aplique~a~distributiva)\\\\7y-23=4y+4~~(some~(-4y)~em~ambos~os~lados~da~igualdade)\\\\7y-23+(-4y)=4y+4+(-4y)\\\\(7y-23)-4y=(4y+4)-4y\\\\(7y-4y)-23=(4y\hspace{-7}\diagup-4y\hspace{-7}\diagup)+4\\\\3y-23=0+4~~(some~23~em~ambos~os~lados~da~igualdade)\\\\3y-23\hspace{-9}\diagup+23\hspace{-9}\diagup=4+23\\\\3y=27~~(multiplique~ambos~os~lados~da~igualdade~por~\dfrac{1}{3})\\\\\dfrac{1}{3}\cdot3y=\dfrac{1}{3}\cdot27\\\\\\\dfrac{3\hspace{-7}\diagup y}{3\hspace{-7}\diagup}=\dfrac{27}{3}\\\\1\cdot y=9$

$\fbox{ y=9 }$

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$4(5y+y)=210\\\\4(6y)=210\\\\32y=210~~(multiplique~ambos~os~lados~da~igualdade~por~\dfrac{1}{32})\\\\\dfrac{1}{32}\cdot32y=\dfrac{1}{32}\cdot210\\\\\\\dfrac{32y}{32}=\dfrac{210}{32}\\\\\\1\cdot y=\dfrac{210}{32}~~(simplifique~a~fra\c{c}\~ao)\\\\\\y=\dfrac{210\div2}{32\div2}\\\\\\\fbox{ y=\dfrac{105}{16} }$

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$3(6+3y)+2=2(y-9)-1~~(aplique~a~distributiva)\\\\(18+9y)+2=(2y-18)-1\\\\(18+2)+9y=(-18-1)+2y\\\\20+9y=-19+2y~~(some~(-2y)~em~ambos~os~lados~da~igualdade)\\\\20+9y+(-2y)=-19+2y+(-2y)\\\\20+(9y-2y)=-19+2y\hspace{-9}\diagup-2y\hspace{-9}\diagup\\\\20+7y=-19~~(some~(-20)~em~ambos~os~lados~da~igualdade)\\\\20+7y+(-20)=-19+(-20)\\\\20+7y-20=(-19-20)\\\\(20\hspace{-9}\diagup-20\hspace{-9}\diagup)+7y=-39\\\\7y=-39~~(multiplica~ambos~os~lados~por~\dfrac{1}{7})\\\\\dfrac{1}{7}\cdot7y=\dfrac{1}{7}\cdot(-39)$

$\dfrac{7\hspace{-7}\diagup y}{7\hspace{-7}\diagup}=-\dfrac{39}{7}\\\\\\1\cdot y=-\dfrac{39}{7}\\\\\\\fbox{ y=-\dfrac{39}{7} }$

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$(9y-5)+4y=(7y+2y)+3\\\\(9y+4y)-5=9y+3\\\\13y-5=9y+3~~(some~(-9y)~em~ambos~os~lados~da~igualdade)\\\\13y-5+(-9y)=9y+3+(-9y)\\\\(13y-5)-9y=(9y+3)-9y\\\\(13y-9y)-5=(9y\hspace{-9}\diagup-9y\hspace{-9}\diagup)+3\\\\4y-5=0+3~~(some~5~em~ambos~os~lados~da~igualdade)\\\\4y-5\hspace{-9}\diagup+5\hspace{-9}\diagup=3+5\\\\4y=8~~(multiplique~ambos~os~lados~da~igualdade~por~\dfrac{1}{4})\\\\\dfrac{1}{4}\cdot4y=\dfrac{1}{4}\cdot8\\\\\\\dfrac{4\hspace{-7}\diagup y}{4\hspace{-7}\diagup}=\dfrac{8}{4}\\\\\\1\cdot y=2$

$\fbox{ y=2 }$