Final answer:
To solve for a when |x+a|=2a and x = -9, substitute x into the equation, yielding two possibilities. One results in a = 9, while the other is not valid. Thus, the value of a is 9.
Step-by-step explanation:
To find the value of a when |x+a|=2a has one solution of x = -9 and a is a positive real number, we start by considering the absolute value equation. The equation |x+a|=2a implies that either x + a = 2a or x + a = -2a. Since x is given as -9, we can substitute this into both potential equations and solve for a.
First, substituting into x + a = 2a:
-9 + a = 2a
a = 9
Then, substituting into x + a = -2a:
-9 + a = -2a
3a = 9, which simplifies to a = 3. However, this second solution creates the inequality |3 + (-9)| = |-6|, which does not equal 2(3), thus it is not valid for the given equation.
Therefore, based on the given information and the solution process, the positive value of a is 9.