Final answer:
The x-value at which f(x) = 2/(5x + 16) and g(x) = 4/(6x + 8) intersect is found by setting the two functions equal, cross-multiplying, and solving for x. The resultant x-value is -6.
Step-by-step explanation:
To find the x-value at which the functions f(x) = 2/(5x + 16) and g(x) = 4/(6x + 8) intersect, we need to set them equal to each other and solve for x.
Setting f(x) equal to g(x) gives us the equation:
2/(5x + 16) = 4/(6x + 8)
To solve for x, cross-multiply to get:
2(6x + 8) = 4(5x + 16)
Simplify and solve for x:
12x + 16 = 20x + 64
Subtract 12x from both sides to get:
16 = 8x + 64
Then, subtract 64 from both sides to find:
-48 = 8x
Finally, divide by 8 to get the value of x:
x = -6
The two functions intersect at x = -6.