if the reciprocal of the opposite of a number, x, is equal to 9 times the opoostie of the number, then the number could be?
To find the number that satisfies the given condition, let's break down the problem step by step.
1. Let's start by identifying the unknown number. In this case, we are given that the unknown number is represented by the variable x.
2. Next, we will translate the given condition into an equation. We are told that the reciprocal of the opposite of x is equal to 9 times the opposite of x. Mathematically, we can represent this as follows:
1/(-x) = 9 * (-x)
3. Simplify the equation further. We can eliminate the negative signs by multiplying both sides of the equation by -1, which gives us:
1/x = -9x
4. To solve for x, we need to isolate it on one side of the equation. Begin by cross-multiplying:
1 = -9x^2
Divide both sides of the equation by -9 to solve for x^2:
x^2 = -1/9
5. Finally, take the square root of both sides of the equation to find the possible values for x:
x = ±√(-1/9)
Simplifying the square root of the negative value, we get:
x = ±(i/3), where i is the imaginary unit.
Therefore, the number that satisfies the given condition can be any complex number of the form ±(i/3), where i represents the square root of -1.