Question

using algebra tiles to model the distributive property
drag tiles to the board to represent the expression.
use algebra tiles to model the expression. then, use the model to help you write an equivalent expression, and complete the statements.
3(x + 1)
model the expression as
groups of x + 1.
there are x tiles.
there are + 1 tiles.
the equivalent expression is .
(board with tiles: +, -, x, -x, and a gray tile; board sum: 0)

Explanation:

Step1: Analyze the expression

The given expression is \( 3(x + 1) \). By the distributive property, \( a(b + c)=ab+ac \), here \( a = 3 \), \( b=x \), \( c = 1 \).

Step2: Determine the number of groups

The expression \( 3(x + 1) \) means there are 3 groups of \( x + 1 \).

Step3: Count the \( x \) tiles

In each group of \( x+1 \), there is 1 \( x \) tile. So for 3 groups, the number of \( x \) tiles is \( 3\times1=3 \).

Step4: Count the +1 tiles

In each group of \( x + 1 \), there is 1 \( + 1 \) tile. So for 3 groups, the number of \( + 1 \) tiles is \( 3\times1 = 3 \).

Step5: Find the equivalent expression

Using the distributive property \( 3(x + 1)=3\times x+3\times1=3x + 3 \).

Answer:

• Model the expression as \( \boldsymbol{3} \) groups of \( x + 1 \).
• There are \( \boldsymbol{3} \) \( x \) tiles.
• There are \( \boldsymbol{3} \) \( + 1 \) tiles.
• The equivalent expression is \( \boldsymbol{3x + 3} \).