Find the number of integers x that satisfy both x² − 7x + 10 ≤ 0 and x² − 9 > 0.

x² − 7x + 10 ≤ 0 factors as (x−2)(x−5) ≤ 0, giving 2 ≤ x ≤ 5. x² − 9 > 0 means (x−3)(x+3) > 0, i.e. x > 3 or x < −3. Intersecting [2,5] with (x>3 or x<−3) leaves 3 < x ≤ 5. The integers in this range are 4 and 5 — exactly 2 values. Always solve each inequality separately on a number line first, then intersect the regions before counting integers.