I was told long ago way back when
that when you have something like this
-x = 7
you solve for x by doing the following
(-x = 7)-
x = -7
but now that I think about it
your not actually multiplying by negative one what is actually happening is this right???
(- x = 7)-^-1
to get the negative ones to cancel out to give you this
x = -^-1 7
or simplified as x = - 7
so my question is does the negative in the denomenator matter??? can you always just move it up or take the opposite of the whole thing even with somehting like this
- x = (7x + 5x^2 - 3)^-1 (6x + 7x^2 -2)
do you sovle this the same way
(- x = (7x + 5x^2 - 3)^-1 (6x + 7x^2 -2))-^-1
x = (-(7x + 5x^2 - 3))^-1 (6x + 7x^2 -2)
is that correct???
my teachers use to tell me that you could just multiply by negative one because it dosen't change its value but that is not true as it changes its direction
Your teachers are right. I do not comprehend your thinking. You are obfuscating a very simple operation, multiplying each side by -1
The equation you provided:
-x = 7
can be solved by applying the concept of isolating the variable x. To do this, you need to get x on one side of the equation.
To isolate x, you can start by multiplying both sides of the equation by -1. However, keep in mind that when you multiply or divide both sides of an equation by a negative number, the inequality sign (if present) would also need to be flipped. In this case, since there is no inequality sign, you can simply multiply both sides by -1.
This gives:
(-1)(-x) = (-1)(7)
Which simplifies to:
x = -7
So, the solution to the equation -x = 7 is x = -7.
Regarding your question about the negative sign in the denominator, it behaves differently than the negative sign in the equation. In general, moving the negative sign from the denominator to the numerator, or vice versa, requires applying the concept of reciprocal, rather than simply taking the opposite.
For example, in your second equation:
- x = (7x + 5x^2 - 3)^-1 (6x + 7x^2 - 2)
To solve this equation, you can start by multiplying both sides by -1:
(-1)(-x) = (-1)(7x + 5x^2 - 3)^-1 (6x + 7x^2 - 2)
Simplifying the left side gives:
x = (-1)(7x + 5x^2 - 3)^-1 (6x + 7x^2 - 2)
Since there is a negative sign in the denominator now, taking the reciprocal of the denominator is necessary.
To do this, you can rewrite the equation as:
x = 1/((7x + 5x^2 - 3) (6x + 7x^2 - 2))
Therefore, the correct way to solve the equation is:
x = 1/((7x + 5x^2 - 3) (6x + 7x^2 - 2))
It's important to keep track of the operations performed on both sides of the equation and follow the rules of algebra to maintain the equality.