Linear Algebra: is it acceptable to make any equation containing $x$ equal $0$?
Is it acceptable to make any equation containing $x$ equal $0$?
For example:
$$\frac{2}{3x + 1}$$
Is it acceptable to make this equation equal zero?
$$\frac{2}{3x + 1} = 0 $$
I'm slightly confused, In my text book it states that the y asymptote of $\frac{2}{3x + 1}$ is $0$, does this mean it is incorrect to ever make this equation equal zero?
Regardless, when is it ok to make an equation equal $0$ and when is it not ok to make an equation equal $0$? (Obviously assuming the equation has an unknown variable in it, $x$)
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$\begingroup$It is fine that you extend your term to an equation.
If the resulting equation has solutions for $x$ which fulfill the equation is not granted. It could have or could have not.
I'm slightly confused, In my text book it states that the $y$ asymptote of $2 / (3x + 1)$ is $0$, does this mean it is incorrect to ever make this equation equal zero?
No. It might give a hint that the equation has no solution. Meaning there is no value for $x$ which satisfies the equation (makes it a true statement).
Regardless, when is it ok to make an equation equal $0$ and when is it not ok to make an equation equal $0$? (Obviously assuming the equation has an unknown variable in it, $x$)
See above. You are allowed to formulate equations.
In case your are interested in solutions for your example: $$ 0 = \frac{2}{3x+1} $$ For any real number $x$ the right hand side will be either positive or negative, but not zero. So there is no solution within the set of real numbers.
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