Question

Solve for x: 3 over 3 x plus 1 over quantity x plus 4 equals 10 over 7x .

Answer 1

3 1 10
------ + --------------- = ----------
3x x +4 7x

1 1 10
------ + ------------ = ----------
x x +4 7x


x + 4 + x 10
------------------ = ----------
x(x +4) 7x

2x + 4 10
------------------ = ----------
x(x +4) 7x

7x(2x + 4) = 10x(x+4)

14x^2 + 28x = 10x^2 + 40x

4x^2 - 12x = 0
4x(x - 3) = 0
4x = 0
x = 0
x - 3 = 0
x = 3

answer x = 0 and x = 3

Answer 2

The value of x is:

3

Explanation:

We are asked to solve:

`(3)/(x)+(1)/(x+4)=(10)/(7x)`

on taking least common multiple in the left hand side of the equation we get:

`(3(x+4)+3x)/(3x(x+4))=(10)/(7x)\\\\\\(3x+12+3x)/(3x(x+4))=(10)/(7x)\\\\\\(6x+12)/(3x(x+4))=(10)/(7x)\\\\\\7x(6x+12)=10(3x(x+4))\\\\\\x(42x+84)=x(30x+120)\\\\\\x(42x+84-30x-120)=0\\\\\\x=0\ or\ 12x-36=0\\\\\\x=0\ or\\\\\\12x=36\\\\\\i.e.\\\\\\x=0\ or\ x=3`

But x≠0

because if x=0 then,

`(1)/(3x)` will not be defined.

Hence, the value of x is:

3