To solve this problem, we need to find the value(s) of [tex]\( x \)[/tex] that satisfy the equation and then determine which of those values must be discarded based on the context of the problem.
The equation given is:
[tex]\[
\frac{1}{x} + \frac{1}{x+5} = \frac{1}{6}
\][/tex]
We solve this equation to find [tex]\( x \)[/tex].
The solutions to the equation are:
[tex]\[
x = -3 \quad \text{and} \quad x = 10
\][/tex]
Next, we need to consider the context to determine which of these solutions makes sense.
- [tex]\( x \)[/tex] represents the number of minutes it takes Mary to wash the car by herself.
A negative value for [tex]\( x \)[/tex] would mean a negative amount of time, which is not physically meaningful in this context. Therefore, [tex]\( x = -3 \)[/tex] must be discarded.
Thus, the correct answer is:
C. [tex]\( x = -3 \)[/tex]
