Which number is a solution of the inequality?
6 greater than z left-parenthesis 10 minus z right-parenthesis
(1 point)
Responses
0
0
1
1
2
2
3
3
To solve the inequality 6 > z(10 - z), we can start by expanding the expression inside the parentheses:
6 > 10z - z^2
Rearranging the terms, we get:
z^2 - 10z + 6 < 0
Now, we can factorize the quadratic equation to get:
(z - 2)(z - 3) < 0
To determine the values of z that make the inequality true, we need to consider the sign of the expression (z - 2)(z - 3).
The product of two factors will be negative if one factor is positive and the other is negative.
So, we have two cases to consider:
1) (z - 2) > 0 and (z - 3) < 0
This means z > 2 and z < 3
2) (z - 2) < 0 and (z - 3) > 0
This means z < 2 and z > 3
However, this case is not possible since it leads to a contradiction.
Therefore, the values of z that satisfy the inequality 6 > z(10 - z) are 2 < z < 3.
None of the given options (0, 1, 2, 3) are solutions to this inequality.