Help me please.. x+4 1 6x =. X

Question

asked Oct 2, 2024 188k views

1 Answer

Milen Kovachev · Answer 1 · 2024-10-08T13:00:37+0000

Hello!

Answer:

$\Large \boxed{\sf x = 2}$

Explanation:

We want to solve this equation:

$\sf (x+4)/(6x) = (1)/(x)$

Let's isolate x.

◼ Multiply both sides by x:

$\sf (x+4)/(6x) * x= (1)/(x) * x$

◼ Simplify both sides:

$\sf (x(x+4))/(6x) = 1$

◼ Simplify the left side:

$\sf (x^2+4x)/(6x) = 1$

◼ Multiply both sides by 6x:

$\sf (x^2+4x)/(6x) * 6x = 1 * 6x$

◼ Simplify both sides:

$\sf x^2+4x =6x$

◼ Subtract 6x from both sides:

$\sf x^2+4x-6x =6x-6x$

◼ Simplify both sides:

$\sf x^2 -2x=0$

It's a quadratic equation because the equation is in the form ax² + bx + c = 0.

The value of x in a quadratic formula is equal to:

$\sf x = (-b \pm √(b^2 -4ac) )/(2a)$

In our equation:

$\sf a =1\\b =-2\\c =0$

Let's solve this quadratic equation:

$\sf x = (-(-2) \pm √((-2)^2 -4 * 1 * 0) )/(2 * 1)$

◼ Simplify the right side:

$\sf x = (2 \pm2 )/(2)$

◼ Find the solutions:

$\sf x = (2+2 )/(2) = (4)/(2) = 2 \\\\\\\sf x = (2 -2 )/(2) = (0)/(2) = 0$

We can't divide by 0 if we replace x by 0 in our equation.

So, the solution of our equation is 2.