Question

select all equations that represent this tape diagram. the tape diagram has a vertical sequence of shapes: x (hexagon), 3 (rectangle), x (hexagon), 3 (rectangle), x (hexagon), 3 (rectangle), x (hexagon), 3 (rectangle), and a vertical rectangle labeled 36 on the right. the options are: 4(x + 12) = 36, 4x + 12 = 36, 4(x + 3) = 36, 4x + 3 = 36 (each with a checkbox).

Explanation:

Step1: Analyze the tape diagram

The tape diagram has 4 groups, each group consists of \( x \) and \( 3 \). So the total of each group is \( x + 3 \), and there are 4 groups, so the equation can be written as \( 4(x + 3)=36 \). Also, if we expand \( 4(x + 3) \), we get \( 4x+12 = 36 \) (since \( 4\times3 = 12 \)).

Step2: Check each equation

• For \( 4(x + 12)=36 \): This would imply each group has \( x + 12 \), which does not match the diagram.
• For \( 4x + 12=36 \): This is the expanded form of \( 4(x + 3) \), so it matches.
• For \( 4(x + 3)=36 \): This matches the group structure (4 groups of \( x + 3 \)).
• For \( 4x + 3=36 \): This would imply 4 \( x \)s and one 3, which does not match the diagram.

Answer:

B. \( 4x + 12 = 36 \)
C. \( 4(x + 3) = 36 \)