Final answer:
To find the variable 'a', we use the relationship FR + RV = FV, with FR = 9a + 2, RV = 34, and FV = 14a - 4. By equating FR + RV to FV and solving for 'a', we find that the value of 'a' is 7.2.
Step-by-step explanation:
The question requires solving for the variable 'a' in the context of line segments on a line. Given FR = 9a + 2, RV = 34, and FV = 14a - 4, you are expected to use the fact that FR + RV = FV because R is a point between F and V on a line segment.
First, write down the equation that represents this relationship:
FR + RV = FV
Substitute the given values:
9a + 2 + 34 = 14a - 4
Solving this equation for 'a' will give us the answer:
36 = 5a
a = 36 / 5
a = 7.2
Therefore, the value of 'a' is 7.2.