Final answer:
The greatest value of x that solves the equation (x)(x−7)(x−17)=0 is 17, as it is the largest value when each factor of the product is set to equal zero.
Step-by-step explanation:
The correct answer is that the greatest value of x which solves the equation (x)(x−7)(x−17)=0 is 17. This equation is a product of three factors set equal to zero. According to the Zero Product Property, if the product of several factors is zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero to find the possible values for x:
- x = 0
- x − 7 = 0 → x = 7
- x − 17 = 0 → x = 17
Comparing the three solutions, we can see that 17 is the largest. Therefore, the greatest value of x that solves the given equation is 17.
The correct answer is option 17, and it represents the highest value of x that solves the equation (x)(x-7)(x-17)=0. To find this, we can set each factor equal to zero and solve for x. So we have x=0, x-7=0, and x-17=0. Solving these equations, we get x=7, x=17, and x=0. Therefore, the greatest value of x that solves the equation is 17.