exam Maths Puzzle Numerical Ability

Please explain this to me. How are proofs in geometry related to logic puzzles?

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The question I have to ask is i don't know understand these problems, do you think you could help me out here? They are:y=12x-4, y=1/4x+3, 3x-y=6, y=-x+2, y=x-3. solve the inequality. write answer in interval notation.
100 < or equal to 10(5x-2) < or equal to 200




for what values of x is the perimeter of the rectangle from 40 to 60 feet?
length:x+3
width: 2x