1. x^2 + 2x - 3 > 0
(x+3)(x-1) > 0
x-intercepts are -3 and 1
so you are looking for the values of x when the parabola y = x^2 + 2x - 3 is above the x-axis
Since it opens upwards those values are
x < -3 OR x > 1
The closest choice to that is #1, but they did not include the necessary OR. The comma is this context means AND, which would be incorrect.
2. 3x^3 + 4x^2 - 59x - 13 > 7
3x^3 + 4x^2 - 59x - 20 > 0
after some quick tries of ±1, ±2, ± 4, I found x=4 to be a solution, so x-4 is a factor
by synthetic division,
3x^3 + 4x^2 - 59x - 20 = (x-4)(3x^2 + 16x + 5)
so the critical values are -5, -1/3, and 4
So the curve is above the x-axis (or above 7 in the original) for
-5 < x < -1/3 OR x > 4
Again, they made an error by not stating the OR condition, but it looks like they meant b) , which is what you had.
3. -5x^2 + 37x> -15x^2 + 12x + 15
10x^2 + 25x - 15 > 0
2x^2 + 5x - 3 > 0
(2x - 1)(x + 3) > 0
critical values are 1/s and -3
so I would check
x < -3, -3 < x < 1/2, and x > 1/2
looks like b) is the correct choice.
1. The graph is a parabola, opening upward. So, there will be a left side and a right side above the x-axis. These intervals will be outside the two roots.
A is the correct answer
2. B is correct
3. The graphs intersect at x = -3 and 0.5
So, B is the answer
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