Final answer:
To determine which television lengths would fit, subtract twice the required speaker space from the total wall length to find the available space for the TV. Televisions equal to or shorter than the available space will fit.
Step-by-step explanation:
Don is planning on mounting a television and wants to ensure it is centered on the wall with specific spacing on each side for external speakers. To determine which television lengths would fit, first, calculate the available space on the wall for the television after accounting for the speakers. Since Don wants at least 24 ½ inches on each side for speakers, we subtract this from the wall's total length:
Total wall length = 88 ¾ inches
Space for each speaker = 24 ½ inches × 2 = 49 inches
Available space for the TV = Total wall length - Space for speakers
= 88 ¾ inches - 49 inches
= 39 ¾ inches available for the television.
Now, we review the lengths of the televisions Don has researched and select all the sizes that are less than or equal to 39 ¾ inches, which would fit on the wall with the desired spacing for the speakers.