Question

select all equations that represent this tape diagram. 2s + 3 = 14, 2s + 6 = 14, 2(s + 6) = 14, 2(s + 3) = 14

Explanation:

Step1: Analyze the tape diagram

The tape diagram has two groups, each group consists of \( s \) and \( 3 \). So the total is \( 2\times(s + 3) \) or expanding it, \( 2s+6 \), and this equals 14.

Step2: Check each equation

• For \( 2s + 3 = 14 \): The constant term should be \( 6 \) (since two 3s), so this is wrong.
• For \( 2s + 6 = 14 \): Expanding \( 2(s + 3) \) gives \( 2s+6 \), so this is correct.
• For \( 2(s + 6) = 14 \): The inside the parentheses should be \( s + 3 \), so this is wrong.
• For \( 2(s + 3) = 14 \): This matches the structure of two groups of \( s + 3 \), so this is correct.

Answer:

\( 2s + 6 = 14 \), \( 2(s + 3) = 14 \)