From the total 1000 students, 450 are male, so 1000 - 450 = 550 students are female.
117 students are both [enrolled in extracurriculars] and [female].
The total number of [female] students is equal to the total number of [female AND enrolled] students plus the total number of [female AND not enrolled] students. The events of being enrolled in extracurriculars and not being enrolled are mutually exclusive. So if <em>x</em> is the number of female students not enrolled in extracurriculars, then