the question is what is the solution of the equation x+2/2=4/x?
1) 1 and-8
2)2 and-4
3) -1 and9
4) -2 and4
I did x^2+2x+8
(x+4)(x+2)
-4 -2
This is not one of the choices
can you help me figure out where I went wrong.
Thanks for your help
I assume you meant
(x+2)/2 = 4/x
multiply each side by 2x , (sometimes called cross-multiplying)
x^2 + 2x = 8
x^2 + 2x - 8 = 0
(x+4)(x-2) = 0
x = -4 OR x = 2 , which is choice 2)
(if the way they presented the answer used the word AND, they they are technically incorrect.
x cannot be -4 AND 2 at the same time, but
x could be -4 OR 2.
btw, you lost your equal sign of the equation, that is where your error occurred.
thank you for your help
To find the solution for the equation x + 2/2 = 4/x, we can start by simplifying the equation.
First, let's multiply both sides of the equation by 2 to get rid of the fraction:
2(x + 2/2) = 2(4/x)
2x + 2 = 8/x
Next, let's multiply both sides of the equation by x to eliminate the fraction:
x(2x + 2) = 8
Expanding the left side:
2x^2 + 2x = 8
Our equation is now in quadratic form. To solve quadratic equations, we can set the equation equal to zero by subtracting 8 from both sides:
2x^2 + 2x - 8 = 0
Now, let's solve this quadratic equation by factoring as you attempted. However, there seems to be a mistake in your factorization. Here's the correct factorization:
2(x^2 + x - 4) = 0
To factorize further, we need to find two numbers whose sum is 1 (the coefficient of x) and whose product is -8 (the constant term multiplied by the coefficient of x^2). The numbers are 4 and -2:
2(x + 4)(x - 1) = 0
Now we can apply the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be zero:
2 = 0 or (x + 4) = 0 or (x - 1) = 0
Since 2 cannot equal zero, we can discard that possibility.
Solving the remaining equations, we get:
x + 4 = 0 => x = -4
x - 1 = 0 => x = 1
So, the correct solutions to the equation x + 2/2 = 4/x are x = -4 and x = 1. However, none of these options matches the given choices (1) 1 and -8, 2) 2 and -4, 3) -1 and 9, 4) -2 and 4). This suggests that either the given choices are incorrect or there may have been a mistake in the equation or the options you provided.