Solve for x and y if x - y = 2 and x\(^2\) - y\(^2\) = 8

If x is inversely proportional to y and x = 2\(\frac{1}{2}\) when y = 2, find x if y = 4

For what range of values of x is \(\frac{1}{2}\)x + \(\frac{1}{4}\) > \(\frac{1}{3}\)x + \(\frac{1}{2}\)?

Solve the inequalities -6 \(\leq\) 4 - 2x < 5 - x

Find the sum to infinity of the following series. 0.5 + 0.05 + 0.005 + 0.0005 + .....