solve the inequality analytically

Question

3x+28<x^2

Answer 1

x² - 3x - 28 > 0; x² - 3x - 28 = 0; x = 7 or x = - 4; So, solution: (- ∞, - 4) U (7, ∞)

Answer 2

3x+28<x²

0<x²-3x-28

0<(x-7)(x+4) This crosses the x-axis at x=7 and x= -4. It opens up because the leading coefficient is 1, which is positive. Therefore the solution to the inequality is x< -4 or x>7