Final answer:
To solve the inequality x² + 8 < 0, there are no real values of x that satisfy the inequality.
Step-by-step explanation:
To solve the inequality x² + 8 < 0, we need to find the values of x that make the expression less than zero. Since the left side of the inequality is a quadratic expression, we can start by setting it equal to zero: x² + 8 = 0. Now we can solve this equation to find the values of x: x² = -8. Taking the square root of both sides, we get x = ∓√-8. However, taking the square root of a negative number results in imaginary solutions, so there are no real values of x that satisfy the inequality. Therefore, the solution to x² + 8 < 0 is the empty set or no solution.