8-2х^2> 0
15х-3х^2<0

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To solve the inequality 8 - 2x^2 > 0:

Add 2x^2 to both sides: 8 > 2x^2Divide by 2: 4 > x^2Take the square root: 2 > x or -2 < x

Therefore, the solution to 8 - 2x^2 > 0 is -2 < x < 2.

To solve the inequality 15x - 3x^2 < 0:

Factor out an x: x(15 - 3x) < 0Set each factor equal to zero: x = 0 or 15 - 3x = 0Solve for x: x = 0 or x = 5

Now, we can test these critical points (x = 0, x = 5) on the inequality x(15 - 3x) < 0:

Test x = -1: (-1)(15 + 3) = -18 < 0Test x = 1: (1)(15 - 3) = 12 > 0Test x = 4: (4)(15 - 12) = 12 > 0Test x = 6: (6)(15 - 18) = -18 < 0

Therefore, the solution to 15x - 3x^2 < 0 is 0 < x < 5.