Question

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

Answer 1

x= 5

x= 8/3

Explanation:

Step one

Given the expression

`(4)/(3x+1) =(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=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-7)\pm√((-7)^2-4*3(-40)))/(2*3)\\\\x=(7\pm√(49+480))/(2*3)\\\\x=(7\pm√(529))/(6)\\\\x=(7\pm 23)/(6)\\\\x=(7\+23)/(6)\\\\x=(30)/(6) \\\\x=5\\\\x=(7-23)/(6)\\\\x=(-16)/(6) \\\\x=(8)/(3)`