Question

Solve the following inequality.
15(x^2 -1)>16x
Select the correct choice below​ and, if​ necessary, fill in the answer box.
A.The solution set is
B.There is no real solution

Answer 1

First, let's simplify the inequality:

15(x^2 - 1) > 16x
15x^2 - 15 > 16x
15x^2 - 16x - 15 > 0

Now, let's factor the quadratic equation:

(3x + 1)(5x - 15) > 0

This simplifies to:

(3x + 1)(x - 3) > 0

Now, we need to find the critical points by setting each factor equal to zero:

3x + 1 = 0
x = -1/3

x - 3 = 0
x = 3

Now, we can use test points to determine the sign of the expression:

Test x = -2: (-) * (-) > 0, false
Test x = 0: (+) * (-) < 0, true
Test x = 4: (+) * (+) > 0, true

Therefore, the solution set for the inequality is:
(-∞, -1/3) U (3, ∞)