Giải bất phương trình sau

To solve this inequality, we need to find the values of x and z that satisfy the inequality.

First, let's rewrite the inequality in standard form:

-x^2 + 3x - z > 0

Next, let's rearrange the terms:

-x^2 + 3x > z

Now, let's find the critical points by setting the left side of the inequality to zero:

-x^2 + 3x = 0

Factor out an x:

x(-x + 3) = 0

Setting each factor to zero:

x = 0 or x = 3

Now, we need to determine the sign of the inequality in the intervals created by the critical points.

For x < 0:

-x^2 + 3x > z is negative since x^2 is positive and 3x is negative. Therefore, this interval does not satisfy the inequality.

For 0 < x < 3:

-x^2 + 3x > z is positive since x^2 is positive and 3x is positive. Therefore, this interval satisfies the inequality.

For x > 3:

-x^2 + 3x > z is negative since x^2 is positive and 3x is positive. Therefore, this interval does not satisfy the inequality.

Therefore, the solution to the inequality is:

0 < x < 3