Question

Which of the following is the solution to 11/(x+2) = 4/(x-1)?

Answer 1

$Solution, \frac{11}{\left(x+2\right)}=\frac{4}{\left(x-1\right)}\quad :\quad x=\frac{19}{7}\quad \left(\mathrm{Decimal:\quad }x=2.71429\dots \right)$

$Steps:$

$\frac{11}{\left(x+2\right)}=\frac{4}{\left(x-1\right)}$

$\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c, 11\left(x-1\right)=\left(x+2\right)\cdot \:4$

$\mathrm{Expand\:}11\left(x-1\right):\quad 11x-11, \mathrm{Expand\:}\left(x+2\right)\cdot \:4:\quad 4x+8, 11x-11=4x+8$

$\mathrm{Add\:}11\mathrm{\:to\:both\:sides}, 11x-11+11=4x+8+11$

$\mathrm{Simplify}, 11x=4x+19$

$\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}, 11x-4x=4x+19-4x$

$Simplify, 7x=19$

$\mathrm{Divide\:both\:sides\:by\:}7, \frac{7x}{7}=\frac{19}{7}$

$\mathrm{Simplify}, x=\frac{19}{7}$

$\mathrm{The\:Correct\:Answer\:is\:D.\:x=\frac{19}{7}}$

$\mathrm{Hope\:This\:Helps!!!}$

$\mathrm{-Austint1414}$