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)
A) l−6.5≤12
B) l−6.5≥12
C) l+6.5≥12
D) l+6.5≤12
D) l+6.5≤12
agree for once
To find the correct inequality that shows the length of a dresser that can be placed against the wall, we need to consider the available space on the wall after placing the bed.
The bed is already along the wall and has a length of 6.5 ft. Therefore, the remaining space on the wall is equal to the total length of the wall minus the length of the bed.
The total length of the wall is 12 ft, and the length of the bed is 6.5 ft. So, the remaining space on the wall is 12 - 6.5 = 5.5 ft.
Now, let's consider the length of the dresser, which we'll represent with the variable "l". For the dresser to fit against the wall, it cannot be longer than the remaining space on the wall, which is 5.5 ft.
This means that the length of the dresser (l) satisfies the inequality l ≤ 5.5.
However, the options provided are not in this format. We can rewrite the inequality as follows:
l + 0 ≤ 5.5
Therefore, the correct inequality that shows the length (l) of a dresser that can be placed against the wall is:
D) l + 6.5 ≤ 12
To find the correct inequality that represents the length (l) of a dresser that can be placed against the wall, we need to consider the available space. The bed already takes up 6.5 ft. of the 12 ft. wall.
Since the dresser needs to fit in the remaining space, we can subtract the length of the bed from the total length of the wall to get the maximum length for the dresser.
Total length of the wall - Length of the bed = Maximum length for the dresser
12 ft - 6.5 ft = 5.5 ft
So, the maximum length for the dresser is 5.5 ft.
Since the inequality is asking for the possible lengths, we use either "less than or equal to" (≤) or "greater than or equal to" (≥).
The dresser can have a length smaller than or equal to 5.5 ft. So, we can represent this as:
l ≤ 5.5
Now we need to rewrite the inequality to take the bed length into consideration:
l + 6.5 ≤ 12
Hence, the correct inequality is option (D) l+6.5≤12.