The range of x that satisfies the inequality is (-3, 5).
To solve the inequality x^2-2x-15<0, find the critical points, divide the number line, and test intervals.
To solve the inequality x2-2x-15<0, we can start by finding the critical points. Set x2-2x-15 equal to zero and solve for x.
The solutions are x = -3 and x = 5. These critical points divide the number line into three intervals: (-∞, -3), (-3, 5), and (5, ∞). We can then test a value from each interval to determine the sign of the expression.
For example, if we choose x = -4 from the interval (-∞, -3), we find that (-4)2-2(-4)-15 = 9, which is positive. Therefore, the range of x that satisfies the inequality is (-3, 5).