Final answer:
The possible values of x for a (x,3),B(7,-1) and AB=5 units are x = 2 or x = 12.
Step-by-step explanation:
To find the possible values of x, we need to calculate the distance between points A(x,3) and B(7,-1). We can use the distance formula, which is given by:
d = sqrt((x-7)^2 + (3-(-1))^2)
Simplifying and squaring both sides of the equation, we get:
d^2 = (x-7)^2 + (4)^2
Since we know that the distance AB is equal to 5 units, we can substitute d = 5 into the equation:
25 = (x-7)^2 + 16
Expanding and rearranging the equation, we find:
0 = x^2 - 14x + 24
Factoring the equation, we get:
0 = (x-2)(x-12)
Setting each factor equal to zero, we find:
x-2 = 0 or x-12 = 0
Therefore, the possible values of x are x = 2 or x = 12.