Question

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Explanation:

Substitute length and width

Using the Polynomial Operations knowledge point, we substitute the length \(l = 3x - 1\) and width \(w = 2x + 4\) into the perimeter formula \(2l + 2w\):

$$ 2(3x - 1) + 2(2x + 4) $$

Distribute the constants

Using the Distributive Property knowledge point, we multiply \(2\) by each term inside the parentheses:

$$ (6x - 2) + (4x + 8) $$

Combine like terms

Using the Like Terms knowledge point, we group and add the variable terms and constant terms:

$$ (6x + 4x) + (-2 + 8) = 10x + 6 $$

Answer:

Question 1

Substitute the expressions for length and width into the formula \(2l + 2w\).
<blank>\(2(3x - 1) + 2(2x + 4)\)</blank>

Question 2

Distribute 2 to each term in the parentheses.
<blank>\(6x - 2 + 4x + 8\)</blank>

Question 3

Combine like terms.
<blank>\(10x + 6\)</blank> inches