Subject: Inequalities
Name: Maleeha
Who are you: Student (Secondary)

a)Use algebra to find the set of values of 'x' for which x(x-5)>36.
b)Using your answer to part a, find the set of values 'y' for which y²(y²-5)>36

Maleeha,

x(x-5)>36 if
x² - 5x - 36 > 0 which is
(x - 9)(x + 4) > 0

The product of two numbers, here (x - 9) and (x + 4), is positive if either both numbers are positive or both numbers are negative. Hence you have two cases to consider:

Case 1: (x - 9) > 0 and (x + 4) > 0

(x - 9) > 0 means x > 9 and x + 4 > 0 means x > -4.
Hence (x - 9) > 0 and (x + 4) > 0 if x > 9 and x > -4.
But this is just x > 9.

Case 2: (x - 9) < 0 and x + 4 < 0

This is yours to complete.

Now can you complete part b?

Penny