Miss Yang has bulletin boards of different sizes in her classroom. She wants to calculate how much border she needs for each one. The length of each bulletin board is 6 inches less than three times its width, w

Question

. Simplify w + 3w − 6 + w + 3w − 6
to find the formula for the perimeter of each of Miss Yang’s bulletin boards.(1 point)

Answer 1

To simplify the expression \( w + 3w - 6 + w + 3w - 6 \), we can first group similar terms.

1. Combine the \( w \) terms: \[ w + 3w + w + 3w = (1 + 3 + 1 + 3)w = 8w \]

2. Combine the constant terms: \[ -6 - 6 = -12 \]

Putting it all together, we get: \[ w + 3w - 6 + w + 3w - 6 = 8w - 12 \]

Now, let's interpret this in terms of the perimeter of the bulletin board. The length \( L \) of the bulletin board is given by: \[ L = 3w - 6 \] The width \( W \) is simply \( w \).

The formula for the perimeter \( P \) of a rectangle is: \[ P = 2L + 2W \] Substituting the values for \( L \) and \( W \): \[ P = 2(3w - 6) + 2w \] Distributing the 2: \[ P = 6w - 12 + 2w \] Combine like terms: \[ P = 8w - 12 \]

Thus, the formula for the perimeter of each of Miss Yang’s bulletin boards, simplified, is: \[ P = 8w - 12 \]