HELP on some problems please?

Question

Questions:

What is the smallest positive integer X such |2-x|>6 (the > symbol have an equal sign)

second question

Greatest prime factor of 520

third question:

Annas ceiling is 16 ft long and 10 ft wide. She is using 2 by 2 tiles to cover it, how many tiles does she need?

Please explain how you got the answers so i can take notes for the future college test.

Answer 1

1.  |2-x| > 6 means 2-x > 6 or 2-x < -6

Solving each inequality gives you

x < -4 or x > 8

The positive part of the solution is x > 8.

The smallest integer that is greater than 8 is 9.

2.  Let's use a factor tree.

_____________ 520

__________ 5 ______ 104

________________ 4 _____ 26

_____________ 2 ___ 2 __2 ___ 13

The prime factors are 2*2*2*5*13, so the greatest prime factor is 13.

3.  The area is 16*10 = 160.

The area of one tile is 2*2 = 4.

160/4 = 40

She needs 40 tiles.