Question
The wall of a bedroom is 12 ft. long. A bed 6.5 ft. in length is already along the wall. Which inequality shows the length ( l ) of a dresser that can also be placed against the wall?(1 point) Responses l+6.5≥12 l plus 6.5 greater-than-or-equal-to 12 l−6.5≥12 l minus 6.5 greater-than-or-equal-to 12 l−6.5≤12 l minus 6.5 less-than-or-equal-to 12 l+6.5≤12
Answers
GPT-4o mini
To determine the inequality that represents the length \( l \) of a dresser that can be placed against the wall without exceeding the total length of 12 ft, we start with the wall length and the bed's length.
The wall is 12 ft long, and the bed occupies 6.5 ft of that space. Therefore, the remaining space for the dresser can be represented as:
\[ l + 6.5 \leq 12 \]
This means the total space occupied by the bed and the dresser cannot exceed 12 ft. Rearranging this inequality, we have:
\[ l \leq 12 - 6.5 \]
\[ l \leq 5.5 \]
The corresponding inequality showing the length \( l \) of the dresser that can also be placed against the wall is:
\[ l + 6.5 \leq 12 \]
So the correct response is:
\[ l + 6.5 \leq 12 \]
The wall is 12 ft long, and the bed occupies 6.5 ft of that space. Therefore, the remaining space for the dresser can be represented as:
\[ l + 6.5 \leq 12 \]
This means the total space occupied by the bed and the dresser cannot exceed 12 ft. Rearranging this inequality, we have:
\[ l \leq 12 - 6.5 \]
\[ l \leq 5.5 \]
The corresponding inequality showing the length \( l \) of the dresser that can also be placed against the wall is:
\[ l + 6.5 \leq 12 \]
So the correct response is:
\[ l + 6.5 \leq 12 \]