Question

a company has two manufacturing plants with daily production levels of 7x + 19 items and 2x - 7 items, respectively. the first plant produces how many more items daily than the second plant? (simplify your answer.) the first plant produces \boxed{} more items daily than the second plant.

Explanation:

Step1: Subtract second plant's production from first

To find how many more items the first plant produces, we subtract the production of the second plant from the first. So we calculate \((7x + 19)-(2x - 7)\).

Step2: Distribute the negative sign

Using the distributive property (also known as the subtraction rule for polynomials), we get \(7x+19 - 2x+7\).

Step3: Combine like terms

Combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(7x-2x = 5x\). For the constant terms: \(19 + 7=26\). So the result is \(5x + 26\).

Answer:

\(5x + 26\)