Question

the steps of an employees calculation for the profit, p(x), are given below. why is the final equation incorrect? use the drop - down menus to explain your answer.
$p(x)=s(x)cdot n(x)-c(x)cdot n(x)$
step 1: $p(x)=x(3,000 - 500x)-1.5(3,000 - 500x)$
step 2: $p(x)=3,000x - 500x^{2}-1.5(3,000 - 500x)$
step 3: $p(x)=3,000x - 500x^{2}-4,500 - 750x$
step 4: $p(x)=-4,500 + 2,250x - 500x^{2}$
click the arrows to choose an answer from each menu.
the first error in the employees calculation occurred in step 3
in that step, choose... . the correct final equation for the profit function sho
a negative was distributed improperly
unlike terms should not have been multiplied
like terms were incorrectly combined

Explanation:

Step1: Analyze Step 3 distribution

Original term: $-1.5(3000 - 500x)$
Correct expansion: $-1.5\times3000 + (-1.5)\times(-500x) = -4500 + 750x$
Employee's result: $-4500 - 750x$

Step2: Identify error type

The negative sign was misapplied to the second term during distribution.

Step3: Derive correct final equation

Start from Step 2: $P(x)=3000x - 500x^2 - 1.5(3000 - 500x)$
Substitute correct expansion:
$P(x)=3000x - 500x^2 - 4500 + 750x$
Combine like terms:
$P(x)=-500x^2 + (3000x+750x) - 4500$
$P(x)=-500x^2 + 3750x - 4500$

Answer:

The first error in the employee's calculation occurred in Step 3.
In that step, a negative was distributed improperly.
The correct final equation for the profit function is $P(x) = -500x^2 + 3750x - 4500$