Question

estion 11.
key
□ = 1
▭ = x
□ (larger) = x²
using the key, which model is equivalent to the expression 3(x + 1)?
four models labeled w, x, y, z
a. w
b. y
c. x
d. z

Explanation:

Step 1: Expand the expression

First, expand \( 3(x + 1) \) using the distributive property. The distributive property states that \( a(b + c)=ab+ac \). So, \( 3(x + 1)=3x + 3 \).

Step 2: Analyze the key and models

From the key: a rectangle (\( \square\)) represents \( x \), a small square (\( \blacksquare\)) represents \( 1 \), and the large square represents \( x^{2} \) (which we don't need here).

• For the expression \( 3x+3 \), we need 3 rectangles (each representing \( x \)) and 3 small squares (each representing \( 1 \)).

Now let's analyze each model:

• Model W: 3 rectangles and 1 small square. This is \( 3x + 1 \), not equal to \( 3x+3 \).
• Model X: 3 rectangles and 3 small squares. This is \( 3x + 3 \), which matches our expanded expression.
• Model Y: 3 small squares and 1 rectangle. This is \( x + 3 \), not equal to \( 3x+3 \).
• Model Z: 1 large square (\( x^{2} \)) and 2 small squares. This is \( x^{2}+2 \), not equal to \( 3x+3 \).

Answer:

C. X