e. \( x^{2}+2 x-15>0 \)

To solve the inequality \( x^{2}+2x-15>0 \), we first find the roots of the corresponding equation \( x^{2}+2x-15=0 \). Factoring gives us \( (x+5)(x-3)=0 \), resulting in roots at \( x=-5 \) and \( x=3 \). We can test the intervals determined by these roots: \( (-\infty, -5) \), \( (-5, 3) \), and \( (3, \infty) \). We find that the expression is positive in the intervals \( (-\infty, -5) \) and \( (3, \infty) \). To visualize this situation, think of a trampoline: the ground is the x-axis, and when you’re below it (negative values), you’re in the dips. However, when you bounce up over the axis (positive values), you’re reaching for the stars! So, here we have our bouncy trampoline going up in those two intervals: \( (-\infty, -5) \) and \( (3, \infty) \).