math help please!!!?

Question

1.find the union and intersection of the following intervals:
a) [-1,2] , [1,4]
b) (-1,4) , [ 3,6)

2.solve for x
⎟⎟x-2⎟-1⎟=1

Answer 1

Q 1 (a)

[-1, 2] ∪ [1, 4] = [-1, 4]
[-1, 2] ∩ [1, 4] = [1, 2]

Q 1 (b)

(-1, 4) ∪ [3, 6) = (-1, 6)
(-1, 4) ∩ [3, 6) = [3, 4)


Q 2

If ||x - 2| -1| = 1, then we must have:
|x - 2| - 1 = -1 or |x - 2| - 1 = 1

so |x - 2| = 0 or |x - 2| = 2

The first of these gives:
x - 2 = 0, so x = 0

The second one gives:
x - 2 = 2 or x - 2 = -2 ⇒ x = 4 or x = 0

∴ solution set is {0, 4}

Answer 2

a. union all the elements in set A or B: [-1;4]
intersection elements in A and B: [1;2]

b. union (-1;6)
intersection [3;4)