If g left parenthesis x right parenthesis equals 36 x squared minus 36 and h left parenthesis x right parenthesis equals 65 x , then solve g left parenthesis x right parenthesis greater than h left parenthesis x right parenthesis.

Given

g (x) = 36x² - 36

h (x) = 65x

Find

x such that g (x) > h (x)

Solution

We can start by substituting the given information into the required relation.

36x² - 36 > 65x

Subtracting the right side and factoring gives

36x² - 65x - 36 > 0

(9x + 4) (4x - 9) > 0

The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = - 4/9 and x = 9/4. Hence, the solution is

x < - 4/9 or 9/4 < x