A convex polyhedron has (a + 3) faces, (2a) vertices, and (4a - 1) edges. What is the value of a? a =

Number of faces: F=a+3

Number of vertices: V=2a

Number of edges: E=4a-1

V+F-E=2

Replacing V=2a; F=a+3; and E=4a-1 in the formula above:

(2a) + (a+3) - (4a-1) = 2

Eliminating parentheses:

2a+a+3-4a+1=2

Adding similar terms:

(2+1-4) a + (3+1) = 2

(-1) a+4=2

Solving for a. Subtracting 4 both sides of the equation:

(-1) a+4-4=2-4

(-1) a=-2

Dividing both sides by (-1)

(-1) a / (-1) = - 2 / (-1)

a=2

Answer: The value of a is: a=2