How will ( [ -6,9]\setminus[-1,4) ) be shown on the number line?

Correct answer: ( [-6,-1)\cup[4,9] )

The direct answer is option A: \([-6,-1)\cup[4,9]\). Set difference means keep the first set and remove every number belonging to the second set. Start with the closed interval \([-6,9]\), which includes both -6 and 9. Remove \([-1,4)\): this removed interval includes -1, includes all numbers up to 4, but does not include 4 itself. The portion left on the left is from -6 through numbers just before -1, so it is \([-6,-1)\): -6 stays, while -1 is removed. The portion left on the right begins at 4 and goes through 9, so it is \([4,9]\): 4 stays because it was excluded from the removed interval, and 9 stays because it belongs to the original interval. Option A is therefore correct. Option B, \([-6,-1]\cup(4,9]\), wrongly keeps -1 and wrongly removes 4. Option C excludes -6 and includes 4 only up to but not including 9, so both endpoint choices are wrong. Option D is a union that overlaps the removed middle part and does not represent subtraction at all. On a number line, shade the original interval, erase the section from -1 including -1 up to but not including 4, and observe the two remaining pieces. Memory cue: in set difference, inspect the brackets at both ends of the part being removed; an included removed endpoint disappears, while an excluded one remains.