To solve this inequality, we first need to find the roots of the quadratic equation -x^2+7x-12=0.
To do this, we can factor the quadratic into (-x+3)(x-4)=0, which gives us the roots x=3 and x=4.
Next, we can use these roots to create intervals on the number line: (-inf, 3), (3, 4), and (4, inf).
For the interval (-inf, 3), we can choose a test point x=0 and evaluate the inequality: -0^2+7(0)-12 < 0, so this interval is a solution.
For the interval (3, 4), we can choose a test point x=3.5 and evaluate the inequality: -3.5^2+7(3.5)-12 <0, so this interval is also a solution.
Finally, for the interval (4, inf), we can choose a test point x=5 and evaluate the inequality: -5^2+7(5)-12 <0, so this interval is not a solution.
Therefore, the solution to the inequality -x^2+7x-12 <0 is x < 3 or 3 < x < 4.
To solve this inequality, we first need to find the roots of the quadratic equation -x^2+7x-12=0.
To do this, we can factor the quadratic into (-x+3)(x-4)=0, which gives us the roots x=3 and x=4.
Next, we can use these roots to create intervals on the number line: (-inf, 3), (3, 4), and (4, inf).
For the interval (-inf, 3), we can choose a test point x=0 and evaluate the inequality: -0^2+7(0)-12 < 0, so this interval is a solution.
For the interval (3, 4), we can choose a test point x=3.5 and evaluate the inequality: -3.5^2+7(3.5)-12 <0, so this interval is also a solution.
Finally, for the interval (4, inf), we can choose a test point x=5 and evaluate the inequality: -5^2+7(5)-12 <0, so this interval is not a solution.
Therefore, the solution to the inequality -x^2+7x-12 <0 is x < 3 or 3 < x < 4.