Answer: Hello there!
We know that the revenue and cost functions are:
R(x) = 16x and C(x) = 12x + 1424
Where x is the number of gidgets sold, now let's calculate the number of gidgets that the company needs to sell if they want to break even:
this means that the diference between the revenue and the cost is zero:
R(x) - C(x) = 0
R(x) = C(x)
16x = 12x + 1424
now let's solve it for x.
16x - 12x = 1424
(16 - 12)x = 1424
4x = 1424
x = 1424/4 = 356
Then the company need to sell at least 356 gidgets.