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 .
1 answer:
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
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
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We will solve the inequality algebraically.
We have then:
We add 2 to both sides of the inequality:
Rewriting we have:
Therefore the solution is:
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Answer:
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See attached image.