Final answer:
To solve the inequality -x²+4x-3<0, first find the critical points and test points in the intervals. The solution set is (1,3).
Step-by-step explanation:
To solve the inequality -x²+4x-3<0, we can first find the critical points of the quadratic function. The critical points occur when the function is equal to zero. So, we set -x²+4x-3=0 and solve for x. We can factor the quadratic equation as (x-3)(-x+1)=0. This gives us x=3 and x=1 as the critical points.
Next, we can choose test points in the intervals defined by the critical points. For example, if we choose x=0, we can plug it into the inequality and see that (-0)²+4(0)-3<0 is true. If we choose x=2, we can plug it in and see that (-2)²+4(2)-3<0 is false. Using this process for each interval, we can determine the solution set of the inequality. In this case, the solution set is (1,3).
Graphing the solution set on a number line, we would shade the interval (1,3) to represent the values of x that satisfy the inequality.