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21. In 4 + In(4x - 15) = In(5x + 19)

User Rebornix
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2 votes

Answer:


x=-30;\quad \:I\\e \:0

Explanation:


In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)


\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\


\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\


\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\\e \:0\\(-nxI)/(-nI)=(30nI)/(-nI);\quad \:I\\e \:0\\\mathrm{Simplify}\\(-nxI)/(-nI)=(30nI)/(-nI)\\\mathrm{Simplify\:}(-nxI)/(-nI):\quad x\\(-nxI)/(-nI)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(-b)=(a)/(b)\\=(nxI)/(nI)\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=(xI)/(I)\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}(30nI)/(-nI):\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:


\quad (a)/(-b)=-(a)/(b)\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=(30I)/(I)\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\\e \:0

User Icasimpan
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