Solve for x in each of the following:
A: 2/3 = x/18
B: 3/x = 3x/x^2
I think I have the first one. I am clueless on the second one! HELP!
Cross multiply to find x.
so...
3/x = 3x/x^2
--> (3*x^2) = (3x*x)
Now simplify.
I still don't get it, where do I simplify at? Fractions aren't my strong point.
actually the 2nd is a strange one, as it has an infinite number of solutions
3/x = 3x/x^2
the right side simplifies to 3/x
so you have 3/x = 3/x, which of course is true for all values of x except x = 0
(remember, we can't divide by zero)
Sure, I can help you with both of these equations.
A: To solve the equation 2/3 = x/18 for x, you can use cross-multiplication.
Cross-multiplying means multiplying the numerator of one fraction by the denominator of the other fraction. In this case, you multiply 2 by 18 and 3 by x.
(2/3) * 18 = (x/18) * 3
36/3 = x
12 = x
Therefore, x = 12 is the solution to the equation.
B: The equation 3/x = 3x/x^2 can be solved by multiplying both sides of the equation by x^2. This will help us eliminate the denominators.
(3/x) * x^2 = (3x/x^2) * x^2
3x = 3x^3
Now, we can rearrange the equation to isolate x.
3x - 3x^3 = 0
Factor out x:
x(3 - 3x^2) = 0
Now, we have two possible solutions:
1. x = 0
2. 3 - 3x^2 = 0
To solve the second equation, we can divide both sides by 3:
3 - 3x^2 = 0
-3x^2 = -3
x^2 = 1
Taking the square root of both sides gives us:
x = ± 1
So, the second equation has two solutions: x = 0 and x = ± 1.
Therefore, the solutions to the equation 3/x = 3x/x^2 are x = 0 and x = ± 1.