Question

solve for the value of x 3x/5x+2=-2​

Answer 1

Answer:

$\dfrac{3x}{5x+2}=-2\quad :\quad x=-\dfrac{4}{13}\quad \left(\mathrm{Decimal}:\quad x=-0.30769\dots \right)$

Step-by-step explanation:

$\dfrac{3x}{5x+2}=-2$

$\black{\mathrm{Simplify\:}\dfrac{3x}{5x+2}\left(5x+2\right):}$

$\dfrac{3x}{5x+2}\left(5x+2\right)=-2\left(5x+2\right)$

$\gray{\mathrm{Multiply\:fractions}:\quad \:a\cdot \dfrac{b}{c}=\dfrac{a\:\cdot \:b}{c}}$

$=\dfrac{3x\left(5x+2\right)}{5x+2}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:5x+2}$

$=3x$

$3x=-2\left(5x+2\right)$

$\black{\mathrm{Expand\:}-2\left(5x+2\right):\quad -10x-4}$

$3x=-10x-4$

$\gray{\mathrm{Add\:}10x\mathrm{\:to\:both\:sides}}$

$3x+10x=-10x-4+10x$

$\gray{\mathrm{Simplify}}$

$13x=-4$

$\gray{\mathrm{Divide\:both\:sides\:by\:}13}$

$\dfrac{13x}{13}=\dfrac{-4}{13}$

$\gray{\mathrm{Simplify}}$

$x=-\dfrac{4}{13}$