Question

Which statement best describes the solutions of this equation? 4/3x+1 = x/2x+10

Answer 1

Answer:

x= 5

x= 8/3

Step-by-step explanation:

Step one

Given the expression

$\frac{4}{3x+1} =\frac{x}{2x+10}$

cross multiply we have

$4(2x+10)= x(3x+1)$

$8x+40=3x^2+x$

collect like terms

$3x^2+x-8x-40=0$

$3x^2-7x-40=0$

applying the quadratic equation

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-7)\pm\sqrt{(-7)^2-4*3(-40)}}{2*3}\\\\x=\frac{7\pm\sqrt{49+480}}{2*3}\\\\x=\frac{7\pm\sqrt{529}}{6}\\\\x=\frac{7\pm 23}{6}\\\\x=\frac{7\+23}{6}\\\\x=\frac{30}{6} \\\\x=5\\\\x=\frac{7-23}{6}\\\\x=\frac{-16}{6} \\\\x=\frac{8}{3}$