To determine the correct expression for the height of the opening for the picture within the frame, let's go through the problem step by step.
1. Understand the Problem:
- The total height of the picture frame is 18 inches.
- There is matting along the periphery of the frame. The height of one side of the matting is represented by [tex]\( m \)[/tex].
2. Visualize the Problem:
- Consider the matting is distributed equally on both the top and bottom sides of the frame.
- Thus, the total height taken up by the matting is [tex]\( m \)[/tex] on the top and [tex]\( m \)[/tex] on the bottom.
3. Calculate the Height of the Opening:
- The total matting height on both sides combined is [tex]\( m + m = 2m \)[/tex].
- Therefore, the height of the opening, which is the remaining height after subtracting the matting, is [tex]\( 18 \)[/tex] inches minus [tex]\( 2m \)[/tex] inches.
4. Formulate the Expression:
- The height of the opening for the picture is [tex]\( 18 - 2m \)[/tex].
Given the problem options, none of them seem to directly match [tex]\( 18 - 2m \)[/tex]. However, this is the correct expression that represents the height of the opening for the picture in the given frame.
Thus, the correct expression representing the height of the opening for the picture is:
[tex]\[ 18 - 2m \][/tex]
(Note: The provided options do not seem to relate directly to the correct expression derived from the problem. However, based on standard mathematical reasoning and interpretation, [tex]\( 18 - 2m \)[/tex] remains the accurate formula.)
