To solve the inequality 4x^2 + 12x > -9, rearrange it to 4x^2 + 12x + 9 > 0, factor as (2x + 3)^2 > 0, and find that all real numbers except x = -3/2 satisfy the inequality. The solution in interval notation is (-∞, -3/2) U (-3/2, ∞).
To solve the inequality 4x^2 + 12x > -9, first we could try to rearrange the inequality to have zero on one side:
4x^2 + 12x + 9 > 0.
Now, we can factor this quadratic expression, if possible, or use the quadratic formula to find the values of x for which the inequality holds. In this case, factorization would result in (2x + 3)^2 > 0, suggesting that all real numbers except x = -3/2 satisfy the inequality, since the square of a real number is always non-negative.
The interval notation for the solution would be (-∞, -3/2) U (-3/2, ∞), which means all real numbers except -3/2 make the inequality true.